General Arithmetic Geometry
[1] The Geometry of the Compactification of the Hurwitz Scheme. PDF Comments NEW !! (2017-08-18)
[2] On Semi-Positivity and Filtered Frobenius Crystals. PDF
[3] Correspondences on Hyperbolic Curves. PDF Comments NEW !! (2024-01-21)
[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 !! (2022-03-20)
[2] Foundations of p-adic Teichmuller Theory. Comments NEW !! (2022-03-20)
[3] An Introduction to p-adic Teichmuller Theory. PDF Comments NEW !! (2022-03-20)
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 Comments NEW !! (2019-06-28)
[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 !! (2022-05-18)
[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 !! (2020-05-18)
[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 !! (2020-05-18)
[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 !! (2024-01-21)
[17] The Geometry of Frobenioids II: Poly-Frobenioids. PDF NEW !! (2008-06-11) Comments NEW !! (2019-02-10)
[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 !!
(2022-03-20) 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 !! (2024-01-21)
[22] Topics in Absolute Anabelian Geometry II: Decomposition Groups and
Endomorphisms. PDF NEW !! (2013-10-08)
Comments NEW !! (2024-01-21)
[23] Topics in Absolute Anabelian Geometry III: Global Reconstruction Algorithms.
PDF NEW !! (2015-11-11) Comments NEW !!
(2019-06-07)
[24] On the Combinatorial Cuspidalization of Hyperbolic Curves. PDF Comments NEW !! (2024-01-21)
[25] On the Combinatorial Anabelian Geometry of Nodally Nondegenerate Outer
Representations. PDF NEW !! (2011-12-22)
Comments NEW !! (2019-07-20)
[26] Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic
Curves I: Inertia Groups and
Profinite Dehn Twists. PDF NEW !! (2012-08-30) Comments NEW !! (2024-01-21)
[27] Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II: Tripods and
Combinatorial Cuspidalization. PDF NEW !! (2022-03-20)
[28] Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic
Curves III: Tripods and
Tempered Fundamental Groups. PDF NEW !! (2023-06-18)
[29] Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic
Curves IV: Discreteness and
Sections. PDF NEW !! (2022-07-31)
[30] Monomorphisms in Categories of Log Schemes. PDF NEW !! (2014-11-24)
[31] Group-theoreticity of Numerical Invariants and Distinguished Subgroups
of Configuration Space Groups. PDF
NEW !! (2021-11-08)
[32] Combinatorial Construction of the Absolute Galois Group of the Field
of Rational Numbers. PDF NEW!! (2024-08-08)
[33] Resolution of Nonsingularities, Point-theoreticity, and Metric-admissibility for p-adic Hyperbolic Curves. PDF
NEW!! (2024-03-31)
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 !! (2020-05-18)
[2] Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic Evaluation.
PDF NEW !! (2020-12-23)
[3] Inter-universal Teichmuller Theory III: Canonical Splittings of the
Log-theta-lattice. PDF NEW !! (2020-05-18)
[4] Inter-universal Teichmuller Theory IV: Log-volume Computations and
Set-theoretic Foundations. PDF
NEW !! (2020-04-22)
[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) Comments NEW !! (2020-04-25)
[7] The Mathematics of Mutually Alien Copies: from Gaussian Integrals
to Inter-universal Teichmuller Theory. PDF
NEW !! (2020-12-23)
[8] Explicit Estimates in Inter-universal Teichmuller Theory. PDF NEW!! (2022-05-18)
[9] On the Essential Logical Structure of Inter-universal Teichmuller Theory
in Terms of Logical AND "∧"/
Logical OR "∨" Relations: Report on the Occasion of the Publication
of the Four Main Papers on
Inter-universal Teichmuller Theory. PDF NEW!! (2024-03-24)
[10] Inter-universal Teichmuller Theory as an Anabelian Gateway to Diophantine
Geometry and Analytic Number Theory
(MFO-RIMS23 Oberwolfach Report). PDF NEW!! (2023-10-20)
