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# Research

# Papers

##
On the Grothendieck conjecture for affine hyperbolic curves over Kummer-faithful fields

RIMS Preprint 1798 (February 2014): Revised Version:
(PDF).

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

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

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

RIMS Preprint 1791 (December 2013): Revised Version:
(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)

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

##
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

RIMS Preprint 1764 (November 2012): Revised Version:
(PDF).

##
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)

to appear in
the Proceedings for Symposium in Durham (July 2011) “Automorphic Forms and Galois Representations”.

##
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.