General Arithmetic Geometry

[1] The Geometry of the Compactification of the Hurwitz Scheme. PDF

[2] On Semi-Positivity and Filtered Frobenius Crystals. PDF

[3] Correspondences on Hyperbolic Curves. PDF Comments NEW !! (2016-07-16)

[4] Extending Families of Curves over Log Regular Schemes. PDF

[5] Noncritical Belyi Maps. PDF Comments NEW !! (2016-07-16)

[6] Arithmetic Elliptic Curves in General Position. PDF NEW !! (2009-02-17) Comments NEW !! (2016-07-16)

Intrinsic Hodge Theory

[1] The Intrinsic Hodge Theory of p-adic Hyperbolic Curves (ICM 98). PDF

[2] The intrinsic Hodge theory of hyperbolic curves (Seoul 1998). PDF

[3] The intrinsic Hodge theory of p-adic hyperbolic curves (Nara 1998). PDF

p-adic Teichmuller Theory

[1] A Theory of Ordinary p-adic Curves. PDF Comments NEW !! (2011-07-15)

[2] Foundations of p-adic Teichmuller Theory. Comments NEW !! (2008-04-09)

[3] An Introduction to p-adic Teichmuller Theory. PDF

Anabelian Geometry, the Geometry of Categories

[1] The Profinite Grothendieck Conjecture for Closed Hyperbolic Curves over
Number Fields. PDF Comments NEW !! (2012-12-20)

[2] A Version of the Grothendieck Conjecture for p-adic Local Fields.
PDF

[3] The Local Pro-p Anabelian Geometry of Curves. PDF

[4] The Grothendieck conjecture on the fundamental groups of algebraic
curves. PDF

[5] The Absolute Anabelian Geometry of Hyperbolic Curves. PDF Comments NEW!! (2016-06-21)

[6] The Absolute Anabelian Geometry of Canonical Curves. PDF Comments NEW !! (2012-06-18)

[7] Topics Surrounding the Anabelian Geometry of Hyperbolic Curves. PDF

[8] The Geometry of Anabelioids. PDF Comments NEW !! (2012-12-20)

[9] Categorical representation of locally noetherian log schemes. PDF Comments NEW !! (2014-10-30)

[10] Categories of log schemes with archimedean structures. PDF PDF (LaTeX Version) Comments NEW !! (2014-10-30)

[11] Semi-graphs of Anabelioids. PDF Comments NEW !! (2016-10-01)

[12] Galois Sections in Absolute Anabelian Geometry. PDF Comments NEW !! (2014-08-09)

[13] A Combinatorial Version of the Grothendieck Conjecture. PDF NEW !! (2007-04-06) Comments NEW !! (2016-06-21)

[14] Conformal and Quasiconformal Categorical Representation of Hyperbolic
Riemann Surfaces. PDF NEW !!

(2006-08-25) Comments NEW !! (2015-12-06)

[15] Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves. PDF PDF (LaTeX Version) NEW !!

(2007-06-06) Comments NEW !! (2014-02-20)

[16] The Geometry of Frobenioids I: The General Theory. PDF NEW !! (2008-06-11) Comments NEW !! (2015-12-06)

[17] The Geometry of Frobenioids II: Poly-Frobenioids. PDF NEW !! (2008-06-11) Comments NEW !! (2015-12-06)

[18] Global Solvably Closed Anabelian Geometry. PDF PDF (LaTeX Version) NEW !! (2006-07-14)

[19] The Etale Theta Function and its Frobenioid-theoretic Manifestations.
PDF NEW !! (2008-12-12) Comments NEW !!

(2016-07-12) Related expositions NEW!! (2015-04-26) Responses to Questions on Frobenioids (cf., especially,

Questions 3, 8, 23, 24) NEW!! (2015-12-06)

[20] The Algebraic and Anabelian Geometry of Configuration Spaces. PDF Comments NEW !! (2015-04-22)

Comments on strongly torsion-free groups NEW !! (2009-02-25)

[21] Topics in Absolute Anabelian Geometry I: Generalities. PDF NEW !! (2012-03-14) Comments NEW !! (2016-10-01)

[22] Topics in Absolute Anabelian Geometry II: Decomposition Groups and
Endomorphisms. PDF NEW !! (2013-10-08)

Comments NEW !! (2016-06-21)

[23] Topics in Absolute Anabelian Geometry III: Global Reconstruction Algorithms.
PDF NEW !! (2015-11-11) Comments NEW !!

(2016-07-12)

[24] On the Combinatorial Cuspidalization of Hyperbolic Curves. PDF Comments NEW !! (2015-02-19)

[25] On the Combinatorial Anabelian Geometry of Nodally Nondegenerate Outer
Representations. PDF NEW !! (2011-12-22)

Comments NEW !! (2016-10-01)

[26] Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic
Curves I: Inertia Groups and

Profinite Dehn Twists. PDF NEW !! (2012-08-30) Comments NEW !! (2015-08-08)

[27] Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II: Tripods and

Combinatorial Cuspidalization. PDF NEW !! (2016-10-24)

[28] Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic
Curves III: Tripods and

Tempered Fundamental Groups. PDF NEW !! (2016-10-24)

[29] Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic
Curves IV: Discreteness and

Sections. PDF NEW !! (2016-10-24)

[30] Monomorphisms in Categories of Log Schemes. PDF NEW !! (2014-11-24)

The Hodge-Arakelov Theory of Elliptic Curves

[1] The Hodge-Arakelov Theory of Elliptic Curves: Global Discretization
of Local Hodge Theories. PDF

[2] The Scheme-Theoretic Theta Convolution. PDF

[3] Connections and Related Integral Structures on the Universal Extension
of an Elliptic Curve. PDF

[4] The Galois-Theoretic Kodaira-Spencer Morphism of an Elliptic Curve.
PDF

[5] The Hodge-Arakelov Theory of Elliptic Curves in Positive Characteristic.
PDF

[6] A Survey of the Hodge-Arakelov Theory of Elliptic Curves I. PDF Comments NEW !! (2012-10-18)

[7] A Survey of the Hodge-Arakelov Theory of Elliptic Curves II. PDF Comments NEW !! (2012-10-18)

[8] Anabelian Geometry in the Hodge-Arakelov Theory of Elliptic Curves.
PDF

Inter-universal Teichmuller Theory

[1] Inter-universal Teichmuller Theory I: Construction of Hodge Theaters.
PDF NEW !! (2017-01-28)

[2] Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic Evaluation.
PDF NEW !! (2017-03-04)

[3] Inter-universal Teichmuller Theory III: Canonical Splittings of the
Log-theta-lattice. PDF NEW !! (2016-12-16)

[4] Inter-universal Teichmuller Theory IV: Log-volume Computations and
Set-theoretic Foundations. PDF

NEW !! (2016-11-12)

[5] A Panoramic Overview of Inter-universal Teichmuller Theory. PDF NEW !! (2013-08-20) Comments NEW !! (2015-11-11)

[6] Bogomolov's Proof of the Geometric Version of the Szpiro Conjecture from the Point of View of

Inter-universal Teichmuller Theory. PDF NEW !! (2016-01-12)

[7] The Mathematics of Mutually Alien Copies: from Gaussian Integrals
to Inter-universal Teichmuller Theory. PDF

NEW !! (2016-12-27)