Papers of Shinichi Mochizuki



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)

List of Papers