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研究

• 論文リスト

• 研究内容紹介 (2024/5/8)

• 2020 年以降の研究の概要 (2024/11/18)

論文

数論幾何学一般

• A note on stable reduction of smooth curves whose Jacobians admit stable reduction (with Shota Tsujimura)
  RIMS Preprint 1964 (August 2022): (PDF).

• On intrinsic Hodge-Tate-ness of Galois representations of dimension two
  Kodai Mathematical Journal (Kodai Math. J.) 47 (2024), no. 1, 99-111.

• A note on fields generated by Jacobi sums
  Mathematical Journal of Okayama University (Math. J. Okayama Univ.) 65 (2023), 117-123.

• A note on Schwarzian derivatives and Sugiyama-Yasuda locally exact differentials
  Osaka Journal of Mathematics (Osaka J. Math.) 61 (2024), no. 3, 313-333.

• Pseudo-rigid p-torsion finite flat commutative group schemes
  Journal of Number Theory (J. Number Theory) 229 (2021), 261-276.

• A note on torsion points on ample divisors on abelian varieties
  Mathematical Journal of Okayama University (Math. J. Okayama Univ.) 64 (2022), 1-11.

• Integrable connections III: Frobenius-descent data
  RIMS Preprint 1904 (July 2019): (PDF).

• Integrable connections II: divided power stratifications
  RIMS Preprint 1903 (July 2019): (PDF).

• Integrable connections I: two fundamental correspondences
  RIMS Preprint 1902 (July 2019): (PDF).

• Homotopy sequences for varieties over curves
  Kobe Journal of Mathematics (Kobe J. Math.) 37 (2020), no. 1-2, 41-66.

• A pro-l version of the congruence subgroup problem for mapping class groups of genus one (with Yu Iijima)
  Journal of Algebra (J. Algebra) 520 (2019), 1-31.

• Corrigendum to “Tame-blind extension of morphisms of truncated Barsotti-Tate group schemes”
  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
  Journal of Mathematical Sciences, The University of Tokyo (J. Math. Sci. Univ. Tokyo) 16 (2009), no. 1, 23-54.

• The exactness of the log homotopy sequence
  Hiroshima Mathematical Journal (Hiroshima Math. J.) 39 (2009), no. 1, 61-121.

遠アーベル幾何学関連 (一般)

• The anabelian geometry of configuration spaces of hyperbolic curves in positive characteristic (with Koichiro Sawada and Shota Tsujimura)
  RIMS Preprint 1984 (May 2024): (PDF).

• Tripod-degrees
  RIMS Preprint 1972 (May 2023): (PDF).

• On the injectivity of the homomorphisms from the automorphism groups of fields to the outer automorphism groups of the absolute Galois groups (with Shota Tsujimura)
  Research in Number Theory (Res. Number Theory) 9 (2023), no. 2, Paper No. 44, 13 pp.

• Galois-theoretic characterization of geometric isomorphism classes of quasi-monodromically full hyperbolic curves with small numerical invariants (with Yu Iijima)
  Journal of Algebra (J. Algebra) 634 (2023), 480-511

• Construction of abundant explicit nongeometric pro-p Galois sections of punctured projective lines (with Shota Tsujimura)
  RIMS Preprint 1950 (June 2021): (PDF).

• Explicit estimates in inter-universal Teichmüller theory (with Shinichi Mochizuki, Ivan Fesenko, Arata Minamide, and Wojciech Porowski)
  Kodai Mathematical Journal (Kodai Math. J.) 45 (2022), no. 2, 175-236.

• The geometry of hyperbolic curvoids
  Publications of the Research Institute for Mathematical Sciences (Publ. Res. Inst. Math. Sci.). 59 (2023), no. 1, 1-55.

• On the geometric subgroups of the étale fundamental groups of varieties over real closed fields (with Takahiro Murotani and Shota Tsujimura)
  Mathematische Zeitschrift (Math. Z.) 298 (2021), no. 1-2, 215-229.

• The absolute anabelian geometry of quasi-tripods
  Kyoto Journal of Mathematics (Kyoto J. Math.) 62 (2022), no. 1, 179-224.

• A note on an anabelian open basis for a smooth variety
  Tohoku Mathematical Journal (Tohoku Math. J.) (2) 72 (2020), no. 4, 537-550.

• The Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one (with Ryo Kinoshita and Chikara Nakayama)
  Kodai Mathematical Journal (Kodai Math. J.) 40 (2017), no. 3, 625-637.

• On the pro-p absolute anabelian geometry of proper hyperbolic curves
  Journal of Mathematical Sciences, The University of Tokyo (J. Math. Sci. Univ. Tokyo) 25 (2018), no. 1, 1-34.

• Categorical characterization of strict morphisms of fs log schemes (with Chikara Nakayama)
  Mathematical Journal of Okayama University (Math. J. Okayama Univ.) 59 (2017), 1-19.

• On the Grothendieck conjecture for affine hyperbolic curves over Kummer-faithful fields
  Kyushu Journal of Mathematics (Kyushu J. Math.) 71 (2017), no. 1, 1-29.

• The pro-l outer Galois actions associated to modular curves of prime power level (with Yu Iijima)
  Journal de Théorie des Nombres de Bordeaux (J. Théor. Nombres Bordeaux) 30 (2018), no. 3, 781-799.

• The Grothendieck conjecture for hyperbolic polycurves of lower dimension
  Journal of Mathematical Sciences, The University of Tokyo (J. Math. Sci. Univ. Tokyo) 21 (2014), no. 2, 153-219.

• Conditional results on the birational section conjecture over small number fields
  Automorphic Forms and Galois Representations. vol. 2, 187-230, London Math. Soc. Lecture Note Ser., 415, Cambridge Univ. Press, Cambridge, 2014.

• On a problem of Matsumoto and Tamagawa concerning monodromic fullness of hyperbolic curves: genus zero case
  Tohoku Mathematical Journal (Tohoku Math. J.) (2) 65 (2013), no. 2, 231-242.

• On monodromically full points of configuration spaces of hyperbolic curves
  The Arithmetic of Fundamental Groups - PIA 2010, 167-207, Contrib. Math. Comput. Sci., 2, Springer, Heidelberg, 2012.

• Existence of nongeometric pro-p Galois sections of hyperbolic curves
  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
  Nagoya Mathematical Journal (Nagoya Math. J.) 203 (2011), 47-100.

• Absolute anabelian cuspidalizations of configuration spaces of proper hyperbolic curves over finite fields
  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
  Mathematical Journal of Okayama University (Math. J. Okayama Univ.) 51 (2009), 1-26.

遠アーベル幾何学関連 (数体や混標数局所体)

• A note on open homomorphisms between global solvably closed Galois groups
  RIMS Preprint 1977 (November 2023): (PDF).

• Homomorphisms of global solvably closed Galois groups compatible with cyclotomic characters (PDF)
  to appear in Tohoku Mathematical Journal (Tohoku Math. J.).

• Mono-anabelian reconstruction of solvably closed Galois extensions of number fields
  Journal of Mathematical Sciences, The University of Tokyo (J. Math. Sci. Univ. Tokyo) 29 (2022), no. 3, 257-283.

• On the outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields (with Yu Nishio)
  Research in Number Theory (Res. Number Theory) 8 (2022), no. 3, Paper No. 56, 13 pp.

• Topics in the anabelian geometry of mixed-characteristic local fields
  Hiroshima Mathematical Journal (Hiroshima Math. J.) 49 (2019), no. 3, 323-398.

• Two categorical characterizations of local fields
  Hiroshima Mathematical Journal (Hiroshima Math. J.) 48 (2018), no. 3, 253-277.

• Mono-anabelian reconstruction of number fields
  RIMS Kôkyûroku Bessatsu B76 (2019), 1-77.

• On the field-theoreticity of homomorphisms between the multiplicative groups of number fields
  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
  Kodai Mathematical Journal (Kodai Math. J.) 36 (2013), no. 2, 284-298.

組み合わせ論的遠アーベル幾何学関連

• Combinatorial construction of the absolute Galois group of the field of rational numbers (with Shinichi Mochizuki and Shota Tsujimura)
  RIMS Preprint 1935 (December 2020): 修正版: (PDF).

• Reconstruction of profinite graphs from profinite groups of PIPSC-type
  Hokkaido Mathematical Journal (Hokkaido Math. J.) 49 (2020), no. 3, 399-430.

• Group-theoreticity of numerical invariants and distinguished subgroups of configuration space groups (with Arata Minamide and Shinichi Mochizuki)
  Kodai Mathematical Journal (Kodai Math. J.) 45 (2022), no. 3, 295-348.

• Topics surrounding the combinatorial anabelian geometry of hyperbolic curves IV: discreteness and sections (with Shinichi Mochizuki)
  Nagoya Mathematical Journal (Nagoya Math. J.) 256 (2024), 785-885.

• Topics surrounding the combinatorial anabelian geometry of hyperbolic curves III: tripods and tempered fundamental groups (with Shinichi Mochizuki) (PDF)
  to appear in Kyoto Journal of Mathematics (Kyoto J. Math.).

• Topics surrounding the combinatorial anabelian geometry of hyperbolic curves II: tripods and combinatorial cuspidalization (with Shinichi Mochizuki)
  Lecture Notes in Mathematics, 2299. Springer, 2022.

• Topics surrounding the combinatorial anabelian geometry of hyperbolic curves I: inertia groups and profinite Dehn twists (with Shinichi Mochizuki)
  Galois-Teichmüller Theory and Arithmetic Geometry, 659-811, Adv. Stud. Pure Math., 63, Math. Soc. Japan, Tokyo, 2012.

• On the combinatorial anabelian geometry of nodally nondegenerate outer representations (with Shinichi Mochizuki)
  Hiroshima Mathematical Journal (Hiroshima Math. J.) 41 (2011), no. 3, 275-342.

通常曲線の理論や p 進 Teichmüller 理論関連

• Canonical liftings of level two of tetrapods in characteristic three (PDF)
  to appear in Kyushu Journal of Mathematics (Kyushu J. Math.).

• On indigenous bundles in characteristic three
  RIMS Preprint 1918 (June 2020): 修正版: (PDF).

• Hyperbolic ordinariness of hyperelliptic curves of lower genus in characteristic three
  Kyushu Journal of Mathematics (Kyushu J. Math.) 73 (2019), no. 2, 317-335.

• On the supersingular divisors of nilpotent admissible indigenous bundles
  Kodai Mathematical Journal (Kodai Math. J.) 42 (2019), no. 1, 1-47.

• Nilpotent admissible indigenous bundles via Cartier operators in characteristic three
  Kodai Mathematical Journal (Kodai Math. J.) 38 (2015), no. 3, 690-731.

正標数双曲的代数曲線の幾何学関連

• An upper bound on the generic degree of the generalized Verschiebung for rank two stable bundles (with Yasuhiro Wakabayashi)
  Journal of Pure and Applied Algebra (J. Pure Appl. Algebra) 228 (2024), no. 6, Paper No. 107605, 14 pp.

• A note on the existence of Tango curves
  Kodai Mathematical Journal (Kodai Math. J.) 44 (2021), no. 1, 77-80.

• Frobenius-affine structures and Tango curves
  Nagoya Mathematical Journal (Nagoya Math. J.) 250 (2023), 385-409

• Frobenius-projective structures on curves in positive characteristic
  Publications of the Research Institute for Mathematical Sciences (Publ. Res. Inst. Math. Sci.). 56 (2020), no. 2, 401-430.

• A note on dormant opers of rank p-1 in characteristic p
  Nagoya Mathematical Journal (Nagoya Math. J.) 235 (2019), 115-126.

双曲的代数曲線の等分点関連

• Ramification of torsion points on a curve with superspecial reduction over an absolutely unramified base
  Tohoku Mathematical Journal (Tohoku Math. J.) (2) 74 (2022), no. 4, 521-534.

• On ramified torsion points on a curve with stable reduction over an absolutely unramified base
  Osaka Journal of Mathematics (Osaka J. Math.) 54 (2017), no. 4, 767-787.

• Finiteness of the moderate rational points of once-punctured elliptic curves
  Hokkaido Mathematical Journal (Hokkaido Math. J.) 45 (2016), no. 2, 271-291.

• On the kernels of the pro-l outer Galois representations associated to hyperbolic curves over number fields
  Osaka Journal of Mathematics (Osaka J. Math.) 52 (2015), no. 3, 647-675.

概説

• 遠アーベル幾何学の進展
  数学 74 (2022), no. 1, 1-30.

• Introduction to mono-anabelian geometry
  Publications mathématiques de Besançon. Algèbre et théorie des nombres. 2021 (Publ. Math. Besançon Algèbre Théorie Nr., 2021), 5-44, Presses Univ. Franche-Comté, Besançon, 2022.

• 続 • 宇宙際 Teichmüller 理論入門
  RIMS Kôkyûroku Bessatsu B72 (2018), 209-307.

• 宇宙際 Teichmüller 理論入門
  RIMS Kôkyûroku Bessatsu B76 (2019), 79-183.

• 組み合わせ論的カスプ化の単射性部分について
  RIMS Kôkyûroku Bessatsu B19 (2010), 81-106.