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

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

[5] Noncritical Belyi Maps. PDF

[6] Arithmetic Elliptic Curves in General Position. PDF NEW !! (2009-02-17) Comments NEW !! (2012-10-08)


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

[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

[10] Categories of log schemes with archimedean structures. PDF

[11] Semi-graphs of Anabelioids. PDF Comments NEW !! (2012-12-20)

[12] Galois Sections in Absolute Anabelian Geometry. PDF

[13] A Combinatorial Version of the Grothendieck Conjecture. PDF NEW !! (2007-04-06) Comments NEW !! (2013-04-12)

[14] Conformal and Quasiconformal Categorical Representation of　Hyperbolic Riemann Surfaces. PDF NEW !!
　　　(2006-08-25)

[15] Absolute Anabelian Cuspidalizations of Proper Hyperbolic Curves. PDF PDF (LaTeX Version) NEW !!
　　　(2007-06-06) Comments NEW !! (2012-10-18)

[16] The Geometry of Frobenioids I: The General Theory. PDF NEW !! (2008-06-11) Comments NEW !! (2012-12-20)

[17] The Geometry of Frobenioids II: Poly-Frobenioids. PDF NEW !! (2008-06-11) Comments NEW !! (2012-12-20)

[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 !!
　　　(2013-02-04)

[20] The Algebraic and Anabelian Geometry of Configuration Spaces. PDF Comments NEW !! (2009-02-25)

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

[22] Topics in Absolute Anabelian Geometry II: Decomposition Groups and Endomorphisms. PDF NEW !! (2013-04-12)

[23] Topics in Absolute Anabelian Geometry III: Global Reconstruction Algorithms. PDF NEW !! (2013-02-04)

[24] On the Combinatorial Cuspidalization of Hyperbolic Curves. PDF Comments NEW !! (2011-04-01)

[25] On the Combinatorial Anabelian Geometry of Nodally Nondegenerate Outer Representations. PDF NEW !! (2011-12-22)
　　　Comments NEW !! (2012-10-25)

[26] Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves I: Inertia Groups and
　　　Profinite Dehn Twists. PDF NEW !! (2012-08-30) Comments NEW !! (2013-05-12)

[27] Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II: Tripods and
　　　Combinatorial Cuspidalization. PDF NEW !! (2013-02-20)

[28] Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves III: Tripods and
　　　Tempered Fundamental Groups. PDF NEW !! (2013-02-20)


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 !! (2013-03-26)

[2] Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic Evaluation. PDF NEW !! (2013-02-20)

[3] Inter-universal Teichmuller Theory III: Canonical Splittings of the Log-theta-lattice. PDF NEW !! (2013-04-24)

[4] Inter-universal Teichmuller Theory IV: Log-volume Computations and Set-theoretic Foundations. PDF
　　NEW !! (2013-03-26)

[5] A Panoramic Overview of Inter-universal Teichmuller Theory. PDF NEW !! (2013-03-26)

List of Papers