List of Papers

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)


Instrinsic 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

[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

[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

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

[8] The Geometry of Anabelioids. PDF

[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 !! (2009-09-03)

[12] Galois Sections in Absolute Anabelian Geometry. PDF

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

[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 !! (2008-02-01)

[16] The Geometry of Frobenioids I: The General Theory. PDF NEW !! (2008-06-11) Comments NEW !! (2008-09-05)

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

[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 !! (2009-05-14)

[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 !! (2008-04-14)

[22] Topics in Absolute Anabelian Geometry II: Decomposition Groups and Endomorphisms. PDF NEW !! (2009-09-03)

[23] Topics in Absolute Anabelian Geometry III: Global Reconstruction Algorithms. PDF NEW !! (2009-04-05)

[24] On the Combinatorial Cuspidalization of Hyperbolic Curves. PDF NEW !! (2009-02-25)

[25] On the Combinatorial Anabelian Geometry of Nodally Nondegenerate Outer Representations. PDF NEW !! (2009-10-01)


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

[7] A Survey of the Hodge-Arakelov Theory of Elliptic Curves II. PDF

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