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Research

A Brief Summary of Some of My Research
A detailed version of “A Brief Summary of Some of My Research” (update: March 7, 2017)
List of Papers

Papers

Frobenius-projective structures on curves in positive characteristic

RIMS Preprint 1871 (April 2017): (PDF).

Group-theoreticity of numerical invariants and distinguished subgroups of configuration space groups (with Arata Minamide and Shinichi Mochizuki)

RIMS Preprint 1870 (March 2017): Revised Version: (PDF).

Introduction to mono-anabelian geometry

RIMS Preprint 1868 (January 2017): (PDF).

On the supersingular divisors of nilpotent admissible indigenous bundles

RIMS Preprint 1867 (December 2016): (PDF).

The Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one (with Ryo Kinoshita and Chikara Nakayama) (PDF)

to appear in Kodai Mathematical Journal (Kodai Math. J.).

On the pro-p absolute anabelian geometry of proper hyperbolic curves

RIMS Preprint 1860 (October 2016): (PDF).

Two categorical characterizations of local fields

RIMS Preprint 1859 (October 2016): (PDF).

Introduction to inter-universal Teichmüller theory, Continued (in Japanese)

PDF (April 2016) (The table of contents in English).

Categorical characterization of strict morphisms of fs log schemes (with Chikara Nakayama) (PDF)

Mathematical Journal of Okayama University (Math. J. Okayama Univ.) 59 (2017), 1-19.

On ramified torsion points on a curve with stable reduction over an absolutely unramified base (PDF)

to appear in Osaka Journal of Mathematics (Osaka J. Math.).

Introduction to inter-universal Teichmüller theory (in Japanese)

PDF (November 2015) (The table of contents in English).

A note on dormant opers of rank p-1 in characteristic p

RIMS Preprint 1822 (April 2015): Revised Version: (PDF).

Mono-anabelian reconstruction of number fields

RIMS Preprint 1819 (March 2015): (PDF).

Nilpotent admissible indigenous bundles via Cartier operators in characteristic three (PDF)

Kodai Mathematical Journal (Kodai Math. J.) 38 (2015), no. 3, 690-731.

On the Grothendieck conjecture for affine hyperbolic curves over Kummer-faithful fields (PDF)

Kyushu Journal of Mathematics (Kyushu J. Math.) 71 (2017), no. 1, 1-29.

Finiteness of the moderate rational points of once-punctured elliptic curves (PDF)

Hokkaido Mathematical Journal (Hokkaido Math. J.) 45 (2016), no. 2, 271-291.

A pro-l version of the congruence subgroup problem for mapping class groups of genus one (with Yu Iijima)

A part of RIMS Preprint 1791 (December 2013): (PDF).

The pro-l outer Galois actions associated to modular curves of prime power level (with Yu Iijima)

A part of RIMS Preprint 1791 (December 2013): (PDF).

Topics surrounding the combinatorial anabelian geometry of hyperbolic curves IV: Discreteness and sections (with Shinichi Mochizuki)

RIMS Preprint 1788 (September 2013): Revised Version: (PDF).

On the kernels of the pro-l outer Galois representations associated to hyperbolic curves over number fields (PDF)

Osaka Journal of Mathematics (Osaka J. Math.) 52 (2015), no. 3, 647-675.

On the field-theoreticity of homomorphisms between the multiplicative groups of number fields (PDF)

Publications of the Research Institute for Mathematical Sciences (Publ. Res. Inst. Math. Sci.) 50 (2014), no. 2, 269-285.

A note on the geometricity of open homomorphisms between the absolute Galois groups of p-adic local fields (PDF)

Kodai Mathematical Journal (Kodai Math. J.) 36 (2013), no. 2, 284-298.

The Grothendieck conjecture for hyperbolic polycurves of lower dimension (PDF)

Journal of Mathematical Sciences, The University of Tokyo (J. Math. Sci. Univ. Tokyo) 21 (2014), no. 2, 153-219.

Topics surrounding the combinatorial anabelian geometry of hyperbolic curves III: Tripods and tempered fundamental groups (with Shinichi Mochizuki)

RIMS Preprint 1763 (November 2012): Revised Version: (PDF).

Topics surrounding the combinatorial anabelian geometry of hyperbolic curves II: Tripods and combinatorial cuspidalization (with Shinichi Mochizuki)

RIMS Preprint 1762 (November 2012): Revised Version: (PDF).

Conditional results on the birational section conjecture over small number fields (PDF)

Automorphic Forms and Galois Representations. vol. 2 (BOOK), 187-230, London Math. Soc. Lecture Note Ser., 415, Cambridge Univ. Press, Cambridge, 2014.

Topics surrounding the combinatorial anabelian geometry of hyperbolic curves I: Inertia groups and profinite Dehn twists (with Shinichi Mochizuki) (PDF)

Galois-Teichmüller Theory and Arithmetic Geometry (BOOK), 659-811, Adv. Stud. Pure Math., 63, Math. Soc. Japan, Tokyo, 2012.

On a problem of Matsumoto and Tamagawa concerning monodromic fullness of hyperbolic curves: Genus zero case (PDF)

Tohoku Mathematical Journal (Tohoku Math. J.) 65 (2013), no. 2, 231-242.

On monodromically full points of configuration spaces of hyperbolic curves (PDF)

The Arithmetic of Fundamental Groups - PIA 2010 (BOOK), 167-207, Contrib. Math. Comput. Sci., 2, Springer, Heidelberg, 2012.

Existence of nongeometric pro-p Galois sections of hyperbolic curves (PDF)

Publications of the Research Institute for Mathematical Sciences (Publ. Res. Inst. Math. Sci.) 46 (2010), no. 4, 829-848.

Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero (PDF)

Nagoya Mathematical Journal (Nagoya Math. J.) 203 (2011), 47-100.

On the combinatorial anabelian geometry of nodally nondegenerate outer representations (with Shinichi Mochizuki) (PDF)

Hiroshima Mathematical Journal (Hiroshima Math. J.) 41 (2011), no. 3, 275-342.

On the injectivity portion of combinatorial cuspidalization (in Japanese) (PDF)

RIMS Kôkyûroku Bessatsu B19 (2010), 81-106.

Corrigendum to “Tame-blind extension of morphisms of truncated Barsotti-Tate group schemes” (PDF)

Journal of Mathematical Sciences, The University of Tokyo (J. Math. Sci. Univ. Tokyo) 19 (2012), no. 3, 309-312.

Tame-blind extension of morphisms of truncated Barsotti-Tate group schemes (PDF)

Journal of Mathematical Sciences, The University of Tokyo (J. Math. Sci. Univ. Tokyo) 16 (2009), no. 1, 23-54.

Absolute anabelian cuspidalizations of configuration spaces of proper hyperbolic curves over finite fields (PDF)

Publications of the Research Institute for Mathematical Sciences (Publ. Res. Inst. Math. Sci.) 45 (2009), no. 3, 661-744.

On the fundamental groups of log configuration schemes (PDF)

Mathematical Journal of Okayama University (Math. J. Okayama Univ.) 51 (2009), 1-26.

The exactness of the log homotopy sequence (PDF)

Hiroshima Mathematical Journal (Hiroshima Math. J.) 39 (2009), no. 1, 61-121.