My Works

I study ARITHMETIC GEOMETRY.
Especially, I am mainly interested in:

$p$-adic Hodge theory and related topics ($(phi,Gamma)$-modules, $p$-adic differential equations...),

Iwasawa theory and Bloch-Kato's Tamagawa number conjecture,

multiple zeta values, fundamental groups, and mixed Tate motives,

Shimura varieties, Drinfel'd modular varieties, moduli of shutkas, and ($p$-adic) Langlands correspondence,

modularity lifting theorems (R=T),

algebraic cycles, mixed motives, and algebraic $K$-theory,

IU Teichmüller theory, and related theories (anabelian geometry, $p$-adic Teichmüller theory...).

Articles

Twisted Heilbronn virtual characters.
to appear in Hokkaido Math. J.

An introduction to $p$-adic Hodge theory for open varieties via syntomic cohomology.
"Une promenade dans la théorie de Hodge $p$-adique: des fondements aux développements récents", Panoramas et Synthèses, 54 (2019), 131--157.

A proof of the abc conjecture after Mochizuki.
preprint. last updated on 8/July/2019.
on the footnote
(* FAQ on Inter-universal Teichmüller Theory)

On finite multiple zeta values of non-positive weight.
preprint.

A simple proof of convolution identities of Bernoulli numbers.
Proc. Japan Acad., 91, Ser. A (2015), 5--6.

A small remark on the filtered $\phi$-module of Fermat varieties and Stickelberger's theorem.
Tsukuba J. Math. vol. 40, No. 1 (2016), 119--124.

A small remark on finite multiple zeta values and $p$-adic multiple zeta values.
RIMS Kôkyûroku Bessatsu, B68 (2017), 171--174.

Reduction of two dimensional crystalline representations and Hypergeometric polynomials.
(with Seidai Yasuda) In preparation.

$p$-adic Hodge theory for open varieties.
Comptes Rendus Math., volume 349 (2011), issues 21-22, 1127--1130.

$p$-adic multiple zeta values, $p$-adic multiple $L$-values, and motivic Galois groups.
"Galois-Teichmüller Theory and Arithmetic Geometry", Adv. Studies in Pure Math. 63 (2012), 629--658.

$p$-adic Lefschetz (1,1) theorem in semistable case, and Picard number jumping locus.
Math. Res. Let. 18 (2011), no. 01, 107--124.

On some applications of integral $p$-adic Hodge theory to Galois representations.
(with Seidai Yasuda) J. Number Theory 147 (2015), 721--748.

Bounds for the dimensions of the $p$-adic multiple $L$-value spaces.
Documenta Math. Extra Volume: Andrei A. Suslin's Sixtieth Birthday (2010) 687--723.

$p$-adic etale cohomology and crystalline cohomology for open varieties with semistable reduction.
(with Seidai Yasuda) preprint.

Presentations (reserch talks and survey talks)

2023

Twisted Heilbronn virtual characters. (40 minutes)
Slides
(26/Sep/2023 at Zoom, Arithmetic Homotopy & Galois Theory, Oberwolfach-RIMS Tandem Workshop)

2022

[CombGC] Part II. (90 minutes)
Slides
(5/Sep/2022 at Zoom, 29th Summer School on Number Theory)

[CombGC] Part I. (90 minutes)
Slides
(5/Sep/2022 at Zoom, 29th Summer School on Number Theory)

Introduction. (90 minutes)
Slides
(5/Sep/2022 at Zoom, 29th Summer School on Number Theory)

2021

A Motivation of Theta-Link from Hodge-Arakelov Theory. (60 minutes)
(31/Aug-3/Sep/2021, 7-10/Sep/2021 at Kyoto University and Zoom, Inter-universal Teichmüller Theory Summit 2021)

2018

ABC Conjecture and Inter-universal Teichmüller Theory. (15 hours in total)
(5-9/Nov/2018 at Keio University, series lectures)

Reductions of crystalline representations and Hypergeometric polynomials. (45 minutes)
(29/June/2018 at Institute for Mathematical Sciences @ the National University of Singapore, Pan Asia Number Theory Conference 2018)

A Proof of the ABC Conjecture after Mochizuki. (45 minutes)
(25/June/2018 at Institute for Mathematical Sciences @ the National University of Singapore, Pan Asia Number Theory Conference 2018)

A Proof of the ABC Conjecture after Mochizuki. (60 minutes)
(18/June/2018 at Institut de Mathématiques de Jussieu, séminaire de théorie des nombres)

2016

Reductions of crystalline representations and Hypergeometric polynomials. (60 minutes)
(16/Nov/2016 at RIMS, Colloquium)

IUTchIII-IV with remarks on the function-theoretic roots of the theory. (4 hours in total)
Slides typeset by RIMS secretariat
(26/Jul/2016 at RIMS, Inter-universal Teichmüller Theory Summit 2016)

2015

IUT-III and IUT-IV section 1 with some remarks on the language of species. (60 minutes)
Slides -> Slides typeset by RIMS secretariat
(11/Dec/2015 at Oxford, Clay Math. Institute Workshop: IUT Theory of Shinichi Mochizuki)

IUT-III. (3 hours in total)
Slides -> Slides typeset by RIMS secretariat
(11/Dec/2015 at Oxford, Clay Math. Institute Workshop: IUT Theory of Shinichi Mochizuki)

Motivation from Hodge-Arakelov Theory. (30 minutes)
(9/Dec/2015 at Oxford, Clay Math. Institute Workshop: IUT Theory of Shinichi Mochizuki)

Inter-universal Teichmuller theory and its Diophantine consequences. (35 hours in total) Pictures of Lectures
(The 3rd week of the series lectures at Kyushu Univ. is merged into this week at RIMS workshop.)
(16-20/Mar/2015 at RIMS, On the verification and further development of inter-universal Teichmuller theory)

Inter-universal Teichmuller theory and its Diophantine consequences. (33.5 hours in total) Pictures of Lectures
(The 2nd week of the series lectures at Kyushu Univ. is merged into this week at RIMS workshop.)
(9-13/Mar/2015 at RIMS, On the verification and further development of inter-universal Teichmuller theory)

2014

Inter-universal Teichmuller theory and its Diophantine consequences--1st week. (18 hours in total)
(16-19/Sep/2014 at Kyushu University, series lectures)

2013

$p$-adic multiple zeta values and motivic Galois groups. (60 minutes)
(25/Jul/2013 at RIMS, Various aspects of multiple zeta values)

On abc Conjecture. (30 minutes)
(non-public talk under the security. I refuse all of inqueries on this talk.)
(6/May/2013 at Toyota Physical and Chemical Research Institute, Colloquium)

Reductions of two dimensional crystalline representations and Hypergeometric polynomials. (60 minutes)
(26/Mar/2013 at Keio University, Number Theory Forum)

$p$-adic multiple zeta values and motivic Galois groups. (60 minutes)
(11/Feb/2013 at Kushu University, Kyushu Algebraic Number Theory 2013)

2012

Etale Cohomology and Weil Conjecture, Part II. (15 hours in total)
(12-16/Nov/2012 at Keio University)

Reductions of two dimensional crystalline representations and Hypergeometric polynomials. (60 minutes)
(12/Sep/2012 at KIAS, Number theory seminar)

Reductions des representations cristallines en dimension deux et Polynomes Hypergeometriques. (60 minutes)
(5/Mar/2012 at Institut de Mathematiques de Jussieu, seminaire de theorie des nombres)

Reduction of two dimensional crystalline representations and Hypergeometric polynomials. (60 minutes)
(2/Mar/2012 at University of Nottingham, Number theory seminar)

Reduction of two dimensional crystalline representations and Hypergeometric polynomials. (60 minutes)
(22/Feb/2012 at Imperial College of London, Number theory seminar)

Wiles' proof of Fermat's Last Theorem for beginners. (50 minutes)
(15/Feb/2012 at Kagoshima University, 7th Kagoshima Algebra-Analysis-Geometry Seminar)
Kagoshima2012small.pdf

2011

Etale Cohomology and Weil Conjecture. (15 hours in total)
(1-5/Nov/2011 at Keio University)

Crystalline cohomology, Universal extension, and $p$-adic Hodge comparison for the $p$-divisible groups. (8 hours in total)
(14-15/Jul/2011 at Hokkaido Univerisity, arithmetic geometry seminar)

$p$-adic multiple zeta values valued in $B_{\mathrm{crys}}$. (90 minutes)
(23/Jun/2011 at Okayama Univerisity, Algebra seminar)

Categories for the working arithmetic geometer. (60 minutes)
(1/Jun/2011 at RIMS, Adventures of Categories -Applied Category Theory Colloquium-)

Automorphy Lifting and integral $p$-adic Hodge theory. (60 minutes)
(25/May/2011 at Keio University, Algebra Seminar)

Automorphy Lifting and integral $p$-adic Hodge theory. (60 minutes)
(22/Apr/2011 at Kyushu University, Algebra Seminar)

local-global compatibility after Barnet-Lamb, Gee, Geraghty, and Taylor. (120 minutes)
(20/Apr/2011 at Kyushu University, arithmetic geometry seminar)

Le relevement d'automorphie et la theorie de Hodge $p$-adique integrale. (60 minutes)
(18/Mar/2011 at Universite de Bordeaux, seminaire de theorie des nombres)

Theorie de Hodge $p$-adique pour les varietes ouvertes. (60 minutes)
(7/Mar/2011 at Institut de Mathematiques de Jussieu, seminaire de theorie des nombres)

Le relevement d'automorphie et la theorie de Hodge $p$-adique integrale. (90 minutes)
(3/Mar/2011 at Institut de Mathematiques de Jussieu, seminaire automorphe)

Pure Mathematics and Applied Mathematics--from a personal point of view--. (50 minutes)
(16/Feb/2011 at Kagoshima University, 6-th Kagoshima Algebra-Analysis-Geometry Seminar)

Gross-Zagier formula. (18 hours in total)
(4-6/Jan/2011 at Hokkaido University, arithmetic geometry seminar)

2010

On the jumping locus of the Picard number. (60 minutes)
(17/Dec/2010 at University of Tokyo, International workshop on motives in Tokyo, part6)

$p$-adic Hodge theory for open varieties. (60 minutes)
(26/Nov/2010 at Osaka University, number theory seminar)

global-local compatibility after Carayol. (120 minutes)
(26/Nov/2010 at Osaka University, number theory preseminar)

$p$-adic multiple zeta values and motivic Galois group. (60 minutes)
(23/Oct/2010 at International Institute for Advances Studies, Galois-theoric Arithmetic Geometry)

Introduction to irreducible admissible representations of GL2 of local fields. (250 minutes)
(3/Aug/2010 at Osaka University, Workshop on arithmetics around GSp(4))

Introduction to $p$-adic Hodge theory. (90 minutes)
(13/Jul/2010 at Nagoya University, Arithmetic Geometry seminar)

Motivic Galois groups and $p$-adic multiple zeta values. (60 minutes)
(9/Feb/2010 at Durham University, Arithmetic Study Group)

2009

Motivic Galois groups and $p$-adic multiple zeta values. (60 minutes)
(17/Dec/2009 at University of Tokyo, International workshop on motives part 5)

$p$-adic Hodge theory for open varieties. (60 minutes)
(13/May/2009 at Cambridge University, algebraic geometry seminar)

$p$-adic multiple zeta values and motivic Galois groups of mixed Tate motives. (60 minutes)
(12/May/2009 at Cambridge University, number theory seminar)

$B_\mathrm{crys}$ lift of $p$-adic Beilinson conjecture. (90 minutes)
(22/Apr/2009 at University of Nottingham, number theory seminar)

Integral $p$-adic Hodge theory and automorphy lifting for unitary groups. (90 minutes)
(14/Jan/2009 at University of Nottingham, number theory seminar)

2008

Bounds for the dimensions of the $p$-adic multiple zeta value space. (60 minutes)
(8/Oct/2008 at Imperial College, number theory seminar)

Kisin's modified Taylor-Wiles system. (60 minutes)
(3/Oct/2008 at University of Nottingham, number theory seminar)

Bounds for the dimensions of the $p$-adic multiple zeta value ($L$-value) space. (90 minutes)
(4/June/2008 at University of Nottingham, number theory seminar)

$p$-adic Hodge theory for open varieties. (60 minutes)
(17/Apr/2008 at University of Nottingham, the Nottingham-Poznan Number theory day)

Proof of Serre's conjecture of level one case after Khare. (90 minutes)
(20/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)

First step of the induction of the proof of Serre's conjecture after Tate, Serre, and Schoof. (90 minutes)
(20/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)

Taylor-Wiles system for unitary groups after Clozel-Harris-Taylor I. (90 minutes)
(19/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)

Modularity lifting of residually reducible case after Skinner-Wiles. (90 minutes)
(19/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)

Modularity lifting for crystalline deformations of intermediate weights after Kisin. (90 minutes)
(18/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)

Modularity lifting for potentially Barsotti-Tate deformations after Kisin I. (90 minutes)
(18/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)
-> Proceding of "Recent Progressions on R=T --Sato-Tate conjecture and Serre's conjecture--"
RT2_yamashita.pdf RT22_errata.pdf (in Japanese)

Galois representations associated to Hilbert modular forms via congruence after Taylor, and Global-local compatibility after Carayol. (90 minutes)
(17/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)

Review of Taylor-Wiles system. (90 minutes)
(17/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)
-> Proceding of "Recent Progressions on R=T --Sato-Tate conjecture and Serre's conjecture--"
RT1_yamashita.pdf RT22_errata.pdf (in Japanese)

2007

$p$-adic multiple zeta value and motivic Galois group. (60 minutes)
(30/Aug/2007 at Queen's University, Departmental Seminar)

Bounds for the dimensions of the $p$-adic multiple zeta value ($L$-value) spaces. (60 minutes)
(25/Jul/2007 at RIMS, Colloquium)

An introduction to Kimura-O'Sullivan's finite dimensionality of pure motives-2. (60 minutes)
(6/Jul/2007 at University of Tokyo, Workshop on Motives III)

An introduction to Kimura-O'Sullivan's finite dimensionality of pure motives-1. (60 minutes)
(3/Jul/2007 at University of Tokyo, Workshop on Motives III)

An introduction to $p$-adic Hodge theory. (8 hours in total)
(14-15/Jun/2007 at Hokkaido University, arithmetic geometry seminar)

Bounds for the dimensions of the $p$-adic multiple zeta value ($L$-value) spaces. (60 minutes)
(4/Jun/2007 at Tambara, $p$-adic aspects in arithmetic geometry)

Bounds for the dimensions of the $p$-adic multiple zeta value ($L$-value) spaces. (60 minutes)
(5/Mar/2007 at Hiroshima University, Motives, related topics, applications)

$p$-adic Hodge theory/$p$-adic multiple zeta values. (Poster)
(14/Feb/2007 at Seoul National University, the 4-th RIMS-SNU Joint Symposium)

2006

$p$-adic Hodge theory for open varieties. (60 minutes)
(21/Nov/2006 at RIMS, $p$-adic Arithmetic Geometry)

$p$-adic Hodge theory for open varieties. (60 minutes)
(11/Oct/2006 at RIMS, Colloquium)

Reduced Power Operations 2. (60 minutes)
(28/Sep/2006 at University of Tokyo, Workshop on Motives II)

Reduced Power Operations 1. (60 minutes)
(27/Sep/2006 at University of Tokyo, Workshop on Motives II)

Review and Overview. (60 minutes)
(25/Sep/2006 at University of Tokyo, Workshop on Motives II)

$p$-adic Hodge theory for open varieties. (60 minutes)
(6/Aug/2006 at University of Tokyo, 51-th Algebra Symposium)
->Proceeding of "51-th Algebra Symposium", p.111-p.131
algsymp2006.dvi algsymp2006.pdf algsymp2006.ps (in Japanese)

Bounds for the dimensions of the $p$-adic multiple zeta value ($L$-value) spaces. (55 minutes)
(4/Jul/2006 at Limoges, le congres Iwasawa 2006)

Bounds for the dimensions of the $p$-adic multiple zeta value (and multiple $L$-value) spaces. (60 minutes)
(26/Apr/2006 at IHES, seminaire de mathematique)

$p$-adic Hodge theory for open varieties (without Faltings' almost etale theory). (60 minutes)
(7/Apr/2006 at Universite Paris 13, seminaire de geometrie arithmetique)

Upper bounds for dimensions of the space of $p$-adic multiple zeta values (and multiple $L$-values). (60 minutes)
(27/Mar/2006 at Institut de Mathematiques de Jussieu, seminaire de theorie des nombres)

$p$-adic Hodge theory for open varieties (without Faltings' almost etale theory). (60 minutes)
(1/Feb/2006 at IHES, seminaire de mathematique)

2005

the category of mixed Tate motives over the ring of integers. (60 minutes)
(21/Dec/2005 at University of Tokyo, Workshop on Motives I)

Introduction to Voevodsky's category of mixed motives 1. (60 minutes)
(19/Dec/2005 at University of Tokyo, Workshop on Motives I)

Bounds for the dimensions of the $p$-adic multiple $L$-value spaces. (60 minutes)
(25/Nov/2005 at University of Tokyo, Tokyo Seoul Conference Arithmetic and Algebraic Geometry)

Bounds for the dimensions of the $p$-adic multiple $L$-value spaces. (30 minutes)
(23/Aug/2005 at Hakui, Number Theory Summer Seminar 2005)
hamahatasan.dvi hamahatasan.pdf hamahatasan.ps

Bounds for the dimensions of the $p$-adic multiple $L$-value spaces. (60 minutes)
(18/May/2005 at Okayama University, Okayama Workshop on Arithmetic and Geometry

2004

Bounds for the dimensions of the $p$-adic multiple $L$-value spaces. (50 minutes)
(6/Dec/2004 at RIMS, Algebraic Number Theory and Related Topics)
-> RIMS kokyu-roku (2005) No.1451, p.37-41.
morishitasan.dvi morishitasan.pdf morishitasan.ps

$p$-adic multiple zeta values, $p$-adic multiple $L$-values, and dimension conjectures. (120 minutes)
(11/Nov/2004 at RIMS, Study of Multiple Zeta Values)
-> RIMS kokyu-roku (2007) No.1549, p.153-168.
ohnosan.dvi ohnosan.pdf ohnosan.ps (in Japanese)

Bounds for the dimensions of the $p$-adic multiple $L$-value spaces. (60 minutes)
(23/Jul/2004 at Hiroshima University, 3-rd Number Theory Symposium)

$p$-adic Hodge theory for open varieties. (60 minutes)
(6/Mar/2004 at Okayama University, 9-th Conference for Young Researchers)
okayama.dvi okayama.ps okayama.pdf (in Japanese)

2003

$p$-adic Hodge theory for open varieties. (15 minutes)
(18/Aug/2003 at Sendai, Number Theory Summer Seminar 2003)
yoinojikan.dvi yoinojikan.ps yoinojikan.pdf (in Japanese)

$p$-adic etale cohomology and crystalline cohomology for open varieties. (60 minutes)
(9/Apr/2003 at Nagoya University, $p$-adic Methods in Number Theory)

$p$-adic etale cohomology and crystalline cohomology for open varieties. (45 minutes)
(14/Mar/2003 at Waseda University, Algebraic Number Theory Symposium)
->Proceeding of "Waseda Algebraic Number Theory Symposium"
waseda.dvi wadeda.ps waseda.pdf

2002

$p$-adic etale cohomology and crystalline cohomology for open varieties. (60 minutes)
(5/Dec/2002 at RIMS, Algebraic Number Theory and Related Topics)
-> RIMS kyokyu-roku (2003) No.1324 p.130-141.
kyoto.dvi kyoto.ps kyoto.pdf

$p$-adic etale cohomology and crystalline cohomology for open varieties. (60 minutes)
(8/Oct/2002 at Hokkaido University, Hodge Theory and Algebraic Geometry)
hokudai.dvi hokudai.ps hokudai.pdf

2001

Introduction to $(\phi,\Gamma)$-modules. (60 minutes)
(6/Dec/2001 at Nagoya University, $p$-adic Representations and $p$-adic Differential Equations)
phigamma.dvi phigamma.ps phigamma.pdf (in Japanese)

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