2014-11-24

・(Papers) Revised version (list of revisions):

Monomorphisms in Categories of Log Schemes.

2014-11-21

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry III.

・(Past and Current Research) Updated the announcement for a workshop

to be held at RIMS during the period March 09〜20, 2015 on IUTeich

(in Japanese). We plan to publish the proceedings (in English) in

the RIMS Kokyuroku Bessatsu series.

2014-11-16

・(Papers) Revised version (list of revisions):

Monomorphisms in Categories of Log Schemes.

・(Past and Current Research) Updated the lecture notes on IUTeich (rela-

tive to the previous 2014-11 version, slightly modified the upper half

of p. 2).

2014-11-12

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

・(Past and Current Research) Updated the lecture notes on IUTeich (rela-

tive to the previous 2014-10 version, slightly modified the upper half

of the following pages: pp. 2, 4).

2014-10-30

・(Papers) Revised version (list of revisions):

Monomorphisms in Categories of Log Schemes.

・(Papers) Updated the comments concerning:

Categorical representation of locally noetherian log schemes.

・(Papers) Updated the comments concerning:

Categories of log schemes with archimedean structures.

・(Past and Current Research) Updated the lecture notes on IUTeich (rela-

tive to the previous 2014-10 version, slightly modified the upper half

of the following pages: pp. 1, 2, 4).

・(Past and Current Research) Posted the announcement for a workshop

to be held at RIMS during the period March 09〜20, 2015 on IUTeich

(in Japanese). We plan to publish the proceedings (in English) in

the RIMS Kokyuroku Bessatsu series.

2014-10-04

・(Past and Current Research) Updated the lecture notes on IUTeich (rela-

tive to the 2014-09 version, slightly modified pp. 4, 13, 14, 17, 18).

2014-09-20

・(Papers) Updated the comments concerning:

Categorical representation of locally noetherian log schemes.

2014-09-15

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

・(Past and Current Research) Posted latest version of lecture notes

on IUTeich (i.e., without any definite plans to give a lecture;

relative to the 2014-05 lecture version, slightly modified p. 4,

p. 9, p. 10, p. 12, p. 13, p. 17).

2014-09-05

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

2014-08-29

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry III.

2014-08-24

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

Inter-universal Teichmuller Theory IV: Log-volume Computations

and Set-theoretic Foundations.

・(Papers) Added the LaTeX version:

Categories of log schemes with archimedean structures.

・(Papers) Updated the comments concerning:

Categorical representation of locally noetherian log schemes.

・(Papers) Updated the comments concerning:

Categories of log schemes with archimedean structures.

2014-08-16

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

2014-08-09

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

Inter-universal Teichmuller Theory IV: Log-volume Computations

and Set-theoretic Foundations.

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry III.

・(Papers) Posted comments concerning:

Topics in Absolute Anabelian Geometry II.

・(Papers) Posted comments concerning:

Galois Sections in Absolute Anabelian Geometry.

2014-07-31

・(Papers) Revised version (list of revisions):

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves IV: Discreteness and Sections.

2014-07-28

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

Inter-universal Teichmuller Theory IV: Log-volume Computations

and Set-theoretic Foundations.

・(Papers) Updated the comments concerning:

Arithmetic Elliptic Curves in General Position.

2014-07-18

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

2014-07-15

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

2014-07-03

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

・(Past and Current Research) Posted a link to an announcement concerning

a lecture series "Inter-universal Teichmuller Theory and its Diophantine

Consequences" (in Japanese) by Go Yamashita.

2014-06-30

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

2014-06-28

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

2014-06-26

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

Inter-universal Teichmuller Theory IV: Log-volume Computations

and Set-theoretic Foundations.

2014-06-14

・(Papers) Revised version (list of revisions):

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves II: Tripods and Combinatorial Cuspidalization.

2014-05-27

・(Travel and Lectures) I made slight modifications to the lecture

notes for the lecture that I gave at Kumamoto University on May 24,

2014 (list of revisions).

2014-05-07

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

2014-04-28

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

・(Papers) New paper:

Monomorphisms in Categories of Log Schemes.

・(Papers) Posted comments concerning:

Categorical representation of locally noetherian log schemes.

・(Papers) Posted comments concerning:

Categories of log schemes with archimedean structures.

2014-04-15

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

2014-04-12

・Uploaded ``Cherry Blossoms around RIMS 2014''.

・(To Prospective Students and Visitors) Updated "To Prospective

Students and Visitors".

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

2014-03-22

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

2014-03-18

・(Travel and Lectures) I made slight modifications to (p. 16, 19 of) the

lecture notes for the lecture to be given at Kumamoto University on May

24, 2014.

2014-03-15

・(Travel and Lectures) Posted the lecture notes for a lecture to be

given at Kumamoto University on May 24, 2014. These lecture notes

are (except for the title) identical to the lecture notes for the lecture

given on February 20, 2014.

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

2014-02-20

・(Travel and Lectures) Posted the lecture notes for a lecture that

I gave today in the RIMS Number Theory Seminar.

・(Past and Current Research) Slightly modified the phrasing (in line 4

of item (7)) of the report released on 2013-12-18 concerning

activities devoted to the verification of IUTeich.

・(Papers) Posted comments concerning:

The Algebraic and Anabelian Geometry of Configuration Spaces.

・(Papers) Updated the comments concerning:

Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry III.

2013-12-28

・(Papers) Revised version (list of revisions):

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves IV: Discreteness and Sections.

2013-12-18

・(Papers) Updated the comments concerning:

The Etale Theta Function and its Frobenioid-theoretic Manifestations.

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory IV: Log-volume Computations

and Set-theoretic Foundations.

・(Past and Current Research) Posted a report concerning activities

devoted to the verification of IUTeich.

2013-11-22

・(Papers) Updated the comments concerning:

The Etale Theta Function and its Frobenioid-theoretic Manifestations.

2013-11-21

・(Papers) Updated the comments concerning:

The Geometry of Frobenioids I: The General Theory.

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

Inter-universal Teichmuller Theory IV: Log-volume Computations

and Set-theoretic Foundations.

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry III.

2013-10-28

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

2013-10-24

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

2013-10-08

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry II.

2013-09-28

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry II.

・(Papers) New paper:

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves IV: Discreteness and Sections.

2013-09-22

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

Inter-universal Teichmuller Theory IV: Log-volume Computations

and Set-theoretic Foundations.

・(Papers) Revised version (list of revisions):

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves II: Tripods and Combinatorial Cuspidalization.

・(Papers) Updated the comments concerning:

Arithmetic Elliptic Curves in General Position.

2013-08-20

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

・(Papers) Revised version (list of revisions):

A Panoramic Overview of Inter-universal Teichmuller Theory.

・(Papers) Updated the comments concerning:

Arithmetic Elliptic Curves in General Position.

2013-07-31

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

Inter-universal Teichmuller Theory IV: Log-volume Computations

and Set-theoretic Foundations.

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry III.

2013-07-17

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry III.

・(Papers) Updated the comments concerning:

The Geometry of Frobenioids I: The General Theory.

・(Papers) Updated the comments concerning:

The Etale Theta Function and its Frobenioid-theoretic Manifestations.

2013-06-28

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry III.

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

・(Papers) Updated the comments concerning:

The Etale Theta Function and its Frobenioid-theoretic Manifestations.

2013-06-08

・(Papers) Revised version (list of revisions):

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves II: Tripods and Combinatorial Cuspidalization.

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory IV: Log-volume Computations

and Set-theoretic Foundations.

2013-05-24

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry III.

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

・(Papers) Updated the comments concerning:

Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.

・(Papers) Posted comments concerning:

The Absolute Anabelian Geometry of Hyperbolic Curves.

2013-05-12

・(Papers) Updated the comments concerning:

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves I: Inertia Groups and Profinite Dehn Twists.

2013-05-02

・(Travel and Lectures) Posted the lecture notes for a lecture to be

given at the University of Tokyo on June 13, 2013. These lecture

notes are based on the survey

A Panoramic Overview of Inter-universal Teichmuller Theory.

that I released a few months ago.

・(Past and Current Research) Posted "FAQ on 'Inter-Universality' "

by Go Yamashita.

2013-04-24

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

2013-04-12

・Uploaded ``Cherry Blossoms around RIMS 2013''.

・(Papers) Updated the comments concerning:

A Combinatorial Version of the Grothendieck Conjecture.

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry II.

・(To Prospective Students and Visitors) Updated "To Prospective

Students and Visitors".

2013-03-26

・(Papers) Revised version (list of revisions):

A Panoramic Overview of Inter-universal Teichmuller Theory.

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

Inter-universal Teichmuller Theory IV: Log-volume Computations

and Set-theoretic Foundations.

2013-03-01

・(Papers) Revised version (list of revisions):

A Panoramic Overview of Inter-universal Teichmuller Theory.

2013-02-21

・(Papers) Revised version (list of revisions):

A Panoramic Overview of Inter-universal Teichmuller Theory.

2013-02-20

・(Papers) New paper (survey of IUTeich):

A Panoramic Overview of Inter-universal Teichmuller Theory.

・(Papers) Revised version (slightly modified the discussion of [Lch] and

updated the references):

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves II: Tripods and Combinatorial Cuspidalization.

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves III: Tripods and Tempered Fundamental Groups.

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

2013-02-04

・(Papers) Updated the comments concerning:

The Etale Theta Function and its Frobenioid-theoretic Manifestations.

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry III.

・(Paper) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

2013-01-14

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

2012-12-26

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

2012-12-20

・(Papers) Updated/posted comments concerning:

The Geometry of Frobenioids I: The General Theory.

The Geometry of Frobenioids II: Poly-Frobenioids.

The Geometry of Anabelioids.

Semi-graphs of Anabelioids.

The Profinite Grothendieck Conjecture for Closed Hyperbolic Curves

over Number Fields.

2012-12-16

・(Papers) Revised version (list of revisions):

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

Inter-universal Teichmuller Theory IV: Log-volume Computations

and Set-theoretic Foundations.

2012-12-02

・(Papers) Updated the comments concerning:

The Geometry of Frobenioids I: The General Theory.

2012-11-28

・(Travel and Lectures) Updated the lecture notes for a lecture to be

given at a workshop scheduled for December 2012.

2012-11-21

・(Travel and Lectures) Updated the lecture notes for a lecture to be

given at a workshop scheduled for December 2012.

・(Papers) Updated the comments concerning:

The Geometry of Frobenioids I: The General Theory.

2012-11-14

・(Papers) Updated the comments concerning:

The Geometry of Frobenioids I: The General Theory.

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry III.

2012-11-10

・(Travel and Lectures) Posted the lecture notes for a lecture to be

given at a workshop scheduled for December 2012. I am scheduled to

write a survey of IUTeich based on these lecture notes by the end

of March 2013.

2012-11-07

・(Papers) New papers:

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves II: Tripods and Combinatorial Cuspidalization.

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves III: Tripods and Tempered Fundamental Groups.

2012-10-25

・(Papers) Posted comments concerning:

On the Combinatorial Anabelian Geometry of Nodally Nondegenerate

Outer Representations.

2012-10-20

・(Papers) Posted comments concerning:

A Combinatorial Version of the Grothendieck Conjecture.

2012-10-18

・(Papers) Revised version (list of revisions):

Topics in Absolute Anabelian Geometry III.

・(Papers) Updated the comments concerning:

Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.

・(Papers) Posted comments concerning:

A Survey of the Hodge-Arakelov Theory of Elliptic Curves I.

A Survey of the Hodge-Arakelov Theory of Elliptic Curves II.

2012-10-14

・(Papers) Posted comments concerning Theorem 1.10 of the following

paper:

Inter-universal Teichmuller Theory IV: Log-volume Computations

and Set-theoretic Foundations.

2012-10-08

・(Papers) Updated the comments concerning:

Arithmetic Elliptic Curves in General Position.

2012-10-06

・(Papers) Posted comments concerning:

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves I: Inertia Groups and Profinite Dehn Twists.

2012-10-02

・(Papers) Updated the comments concerning:

The Etale Theta Function and its Frobenioid-theoretic Manifestations.

2012-08-30

・(Papers) Revised version (the revisions are minor and unrelated to

the substantive content of the paper):

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves I: Inertia Groups and Profinite Dehn Twists.

・(Papers) New papers:

Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.

Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic

Evaluation.

Inter-universal Teichmuller Theory III: Canonical Splittings of

the Log-theta-lattice.

Inter-universal Teichmuller Theory IV: Log-volume Computations

and Set-theoretic Foundations.

2012-06-18

・(Papers) Posted comments concerning:

The Absolute Anabelian Geometry of Canonical Curves.

2012-04-14

・Uploaded ``Cherry Blossoms around RIMS 2012''.

2012-04-12

・(Papers) Revised version (made slight modifications to Theorem

1.8, (i); Corollary 1.11, (i); the Bibliography)

Topics in Absolute Anabelian Geometry II.

2012-04-06

・(Papers) Revised version (the revisions are minor and unrelated to

the mathematical content of the paper):

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves I: Inertia Groups and Profinite Dehn Twists.

2012-04-05

・(Top page) Replaced the photograph on the top page by a photograph

taken a few days ago.

2012-04-02

・(To Prospective Students and Visitors) Updated "To Prospective

Students and Visitors".

2012-03-14

・(Papers) Revised version (list of main revisions):

Topics in Absolute Anabelian Geometry I.

2012-02-12

・(Papers) Revised version (list of main revisions):

Topics in Absolute Anabelian Geometry I.

Topics in Absolute Anabelian Geometry II.

Topics in Absolute Anabelian Geometry III.

2012-01-23

・(Thoughts) Posted a report concerning my progress in writing up

my ideas on IUTeich theory.

2011-12-22

・(Papers) Revised version (in which we corrected a misprint in

Lemma 1.5):

On the Combinatorial Anabelian Geometry of Nodally Nondegenerate

Outer Representations.

2011-11-25

・(Papers) Updated the comments concerning:

The Geometry of Frobenioids I: The General Theory.

2011-11-08

・(Papers) Upon receiving notification that in certain computing

environments the PDF files in the present site are unreadable, I

decided to replace most of the PDF files in the present site by

``font embedded versions''.

・(Safety Confirmation Information) I added a ``Safety Confirmation

Information'' button to the present page in the hope that it might

be of use in emergency situations such as natural disasters.

2011-09-08

・(Papers) Updated the comments concerning:

The Etale Theta Function and its Frobenioid-theoretic Manifestations.

2011-07-15

・(Papers) Posted comments concerning:

A Theory of Ordinary p-adic Curves.

・(Papers) Posted comments concerning:

Arithmetic Elliptic Curves in General Position.

2011-06-20

・(Thoughts) Posted a report concerning my progress in writing up

my ideas on IUTeich theory.

2011-05-02

・(Thoughts) I realized that the valuation-theoretic problem left

pending in my comments of 2011-03-03 may be resolved quite easily.

In particular, one may derive the main theorem obtained in Pop-Stix'

work on the p-adic Section Conjecture as a consequence of an entirely

elementary argument in graph theory and commutative algebra (i.e.,

without resorting to the use of difficult arithmetic results such

as Tamagawa's ``resolution of nonsingularities''). Click here for

more details.

2011-04-12

・Uploaded ``Cherry Blossoms around RIMS 2011''.

2011-04-01

・(Papers) New paper:

Topics Surrounding the Combinatorial Anabelian Geometry of

Hyperbolic Curves I: Inertia Groups and Profinite Dehn Twists.

・(Papers) Posted comments concerning:

On the Combinatorial Cuspidalization of Hyperbolic Curves.

2011-03-03

・(Thoughts) As I explained in a previous note, one may apply the work

of Pop-Stix on the p-adic Section Conjection to reduce the Profinite

p-adic Section Conjecture to its tempered counterpart (a remark

due to Y. Andre). On the other hand, I recently noticed that this

reduction may also be obtained as a consequence of an entirely

elementary graph-theoretic argument (i.e., without resorting to

the use of difficult arithmetic results such as Tamagawa's

``resolution of nonsingularities''). Click here for more details.

2010-11-23

・(Papers) Updated the comments concerning:

Semi-graphs of Anabelioids.

2010-11-18

・(Thoughts) Posted a report concerning my progress in writing up

my ideas on IUTeich theory.

2010-11-15

・(Thoughts) Again I made slight modifications to my comments the

other day concerning the the theorem of Pop-Stix and updated the

various links for these comments to the latest version.

・(Papers) Updated the comments concerning:

Semi-graphs of Anabelioids.

2010-11-11

・(Thoughts) I made slight modifications to my comments the other

day concerning the the theorem of Pop-Stix. Click here for more

details.

・(Papers) Revised version (in which we made slight modifications to

the discussion of the relationship to the work of Takao):

On the Combinatorial Anabelian Geometry of Nodally Nondegenerate

Outer Representations.

2010-11-02

・(Thoughts) I realized, with regard to the relationship between the

``combinatorial section conjecture'' and the work of Pop-Stix on

the p-adic Section Conjection, that a similar argument holds over

more general fields and for more general sets of primes Σ. This

lead me to modify the argument I gave on 2010-10-29. Click here

for more details.

2010-10-29

・(Thoughts) I recently realized that the work of Pop-Stix on the

p-adic Section Conjecture is related to the ``combinatorial

section conjecture'' that I proved in my paper ``Semi-graphs of

anabelioids'' a few years ago. Click here for more details.

2010-10-27

・(Papers) Revised version (in which I replaced statements

concerning the ``genus'' by statements concerning the ``type'' in

Definition 1.9; Corollaries 1.10, 1.11):

Topics in Absolute Anabelian Geometry II.

2010-10-13

・(Travel and Lectures) Posted the lecture notes for a lecture to be

given at a workshop scheduled for October 2010.

・(To Prospective Students and Visitors) Updated "To Prospective

Students and Visitors".

2010-07-16

・(Past and Current Research) Posted the abstract of a lecture to be

given at a workshop scheduled for October 2010.

2010-06-18

・(Papers) Revised version (in which I made slight modifications to

Propositions 5.7, (ii); 5.8, (vi)):

Topics in Absolute Anabelian Geometry III.

2010-06-11

・(Papers) Revised version (in which I made a slight modification to

Definition 5.4, (v)):

Topics in Absolute Anabelian Geometry III.

2010-06-01

・(Papers) Revised version (in which I modified Corollary 2.8, (i),

and Remark 2.12.1):

Topics in Absolute Anabelian Geometry I.

2010-05-06

・(Papers) Revised version (list of main revisions):

Topics in Absolute Anabelian Geometry I.

2010-04-12

・(Thoughts) Posted a report concerning my progress in writing up

my ideas on IUTeich theory.

・Uploaded ``Cherry Blossoms around RIMS 2010''.

2009-10-15

・(Thoughts) Posted a report concerning my progress in writing up

my ideas on IUTeich theory.

・(To Prospective Students and Visitors) Updated "To Prospective

Students and Visitors".

2009-10-01

・(Papers) Revised version (in which we modified Lemma 1.6, Remark

1.6.1):

On the Combinatorial Anabelian Geometry of Nodally Nondegenerate

Outer Representations.

2009-09-13

・(Papers) Revised version (in which we modified Theorem 6.1, Corollary 6.3):

On the Combinatorial Anabelian Geometry of Nodally Nondegenerate

Outer Representations.

2009-09-03

・(Papers) Updated the comments concerning:

Semi-graphs of Anabelioids.

・(Papers) Revised version (in which I made a slight modification

to Remark 2.11.1):

Topics in Absolute Anabelian Geometry II.

2009-08-19

・(Papers) New paper:

On the Combinatorial Anabelian Geometry of Nodally Nondegenerate

Outer Representations.

2009-07-06

・(Papers) Revised version (in which I made a slight modification

concerning the term ``edge-paired'' in the case in which the

prime under consideration is equal to 2):

Topics in Absolute Anabelian Geometry II.

2009-06-16

・(Papers) Updated the comments concerning:

Semi-graphs of Anabelioids.

2009-05-14

・(Papers) Posted comments concerning:

The Etale Theta Function and its Frobenioid-theoretic Manifestations.

2009-04-21

・(Papers) Revised version (in which I added Remark 2.11.1):

Topics in Absolute Anabelian Geometry II.

2009-04-12

・Uploaded ``Cherry Blossoms around RIMS 2009''.

2009-04-05

・(Papers) Revised version (in which I revised the definition of a log-shell):

Topics in Absolute Anabelian Geometry III.

2009-02-25

・(Papers) Revised version:

On the Combinatorial Cuspidalization of Hyperbolic Curves.

・(Papers) Posted comments related to the content of the following

paper:

The Algebraic and Anabelian Geometry of Configuration Spaces.

2009-02-17

・(Papers) Revised version:

Arithmetic Elliptic Curves in General Position.

2009-02-11

・(Thoughts) Posted a report concerning my progress in writing up

my ideas on IUTeich theory.

2009-01-22

・(Papers) Revised version:

On the Combinatorial Cuspidalization of Hyperbolic Curves.

2008-12-12

・(Papers) Updated the list of papers and posted revised version:

The Etale Theta Function and its Frobenioid-theoretic Manifestations.

2008-11-17

・(Papers) Revised version:

The Etale Theta Function and its Frobenioid-theoretic Manifestations.

2008-09-05

・(Papers) Posted comments concerning:

The Geometry of Frobenioids I: The General Theory.

2008-08-18

・(Papers) Revised version:

Topics in Absolute Anabelian Geometry II.

2008-08-03

・(Papers) Revised version:

Topics in Absolute Anabelian Geometry III.

2008-07-21

・(Past and Current Research) ''So what is IUTeich theory about?''

an explanation via ``Sokkuri animation'' that was pointed out to

me by Fumiharu Kato.

2008-06-17

・(Papers) Revised version:

Arithmetic Elliptic Curves in General Position.

2008-06-11

・(Papers) New paper:

On the Combinatorial Cuspidalization of Hyperbolic Curves.

・(Papers) Revised version:

The Geometry of Frobenioids I: The General Theory.

・(Papers) Revised version:

The Geometry of Frobenioids II: Poly-Frobenioids.

・(Thoughts) Added a report on recent research concerning

combinatorial cuspidalization and absolute pro-p anabelian

geometry.

2008-05-18

・(Travel and Lectures) Posted the lecture notes for my lectures for

students and colloquium talk on ``Arithmetic Teichmuller Theory''

(in Japanese)

・(Papers) Updated the picture in the paper as well as the comments

concerning:

Semi-graphs of Anabelioids.

2008-04-14

・(Papers) Revised version:

Topics in Absolute Anabelian Geometry I, II, III.

2008-04-09

・Uploaded ``Cherry Blossoms around RIMS 2008''.

・(Thoughts) Added a report on research concerning a combinatorial

version of an injectivity theorem of Matsumoto.

・(Papers) Posted comments concerning:

Foundations of p-adic Teichmuller Theory.

・(Papers) Posted comments concerning:

Semi-graphs of Anabelioids.

2008-03-25

・(Papers) New series of papers:

Topics in Absolute Anabelian Geometry I, II, III.

・(Papers) New paper:

Arithmetic Elliptic Curves in General Position.

・(Past and Current Research) Updated the report on my research up

till now.

2008-02-01

・(Papers) Posted comments concerning:

Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.

2008-01-05

・(Papers) Revised version:

The Geometry of Frobenioids I: The General Theory.

・(Papers) Revised version:

The Geometry of Frobenioids II: Poly-Frobenioids.

2007-07-27

・(Papers) Revised version:

The Algebraic and Anabelian Geometry of Configuration Spaces.

2007-06-06

・(Papers) Revised version:

Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.

2007-05-16

・(Papers) Revised version:

The Geometry of Frobenioids I: The General Theory.

・(Papers) Revised version:

The Geometry of Frobenioids II: Poly-Frobenioids.

・(Papers) Revised version:

The Etale Theta Function and its Frobenioid-theoretic Manifestations.

2007-04-12

・Uploaded ``Cherry Blossoms around RIMS 2007''.

2007-04-06

・(Papers) Revised version:

A Combinatorial Version of the Grothendieck Conjecture.

2007-01-31

・(Papers) Revised version:

Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.

・(Papers) Revised version:

A Combinatorial Version of the Grothendieck Conjecture.

2007-01-20

・(Papers) Revised version:

Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.

2006-12-23

・(Papers) Revised version:

Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.

・(Papers) Revised version:

The Geometry of Frobenioids I: The General Theory.

・(Papers) Revised version:

The Geometry of Frobenioids II: Poly-Frobenioids.

・(Papers) Revised version:

The Etale Theta Function and its Frobenioid-theoretic Manifestations.

2006-11-27

・(Papers) Revised version:

The Algebraic and Anabelian Geometry of Configuration Spaces.

2006-11-18

・(Travel and Lectures) Posted the lecture notes for my lecture at

the workshop on ``p-adic Arithmetic Geometry'' to be held next week.

2006-10-31

・(Thoughts) Erratum concerning ``symmetrized configuration

spaces''.

2006-09-16

・(Past and Current Research) Updated the report on my recent

research related to the ABC Conjecture.

2006-09-06

・(Papers) New paper:

The Algebraic and Anabelian Geometry of Configuration Spaces.

2006-09-01

・(Papers) Revised version:

The Etale Theta Function and its Frobenioid-theoretic Manifestations.

2006-08-25

・(Thoughts) More on recent work in anabelian geometry.

・(Papers) Revised version:

Conformal and Quasiconformal Categorical Representation of

Hyperbolic Riemann Surfaces.

2006-07-14

・(Papers) Revised version:

Global Solvably Closed Anabelian Geometry.

2006-06-24

・(Thoughts) Added a report on recent work in anabelian geometry.

2006-06-13

・(Papers) Revised version:

The Geometry of Frobenioids I: The General Theory.

2006-06-03

・(Papers) Revised version:

Global Solvably Closed Anabelian Geometry.

2006-06-02

・(To Prospective Students and Visitors) Updated "To Prospective

Students and Visitors".

2006-05-22

・(Curriculum Vitae) Added an mp3 file that contains the

pronunciation of my name.

2006-05-21

・(Papers) Revised version:

Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves.

2006-04-22

・(Papers) New paper:

The Etale Theta Function and its Frobenioid-theoretic Manifestations.

2006-04-11

・(Papers) Revised version:

A Combinatorial Version of the Grothendieck Conjecture.

・(Papers) Revised version:

The Geometry of Frobenioids I: The General Theory.

・(Papers) Revised version:

The Geometry of Frobenioids II: Poly-Frobenioids.

2006-04-06

・(Papers) Revised version:

Conformal and Quasiconformal Categorical Representation of

Hyperbolic Riemann Surfaces.