research interests: Galois representations, finite flat group schemes, integral p-adic Hodge theory, ramification, modular forms

news

	I'll be away from Fukuoka during Jun. 5--8 and 17--24. (May 7, 2012)

	[代数学セミナー/ Algebra seminar] The website is here. [数論幾何学セミナー/ Arithmetic geometry study group seminar] is now operated by Takahiro Tsushima. An old website until 2011 is here. A list (in Japanese) of upcoming conferences of my interest is here. The workshop "Industrious Number Theory" had been held during Dec. 4-5, 2009. I would like to thank all the speakers and participants. The website is here.

	On a ramification bound of torsion semi-stable representations over a local field, J. of Number theory 129 (2009), 2474-2503 abs
		Let k be a perfect field of characteristic p>0, K_0=Frac(W(k)) and K be a finite totally ramified extension of K_0 of degree e. Let r be a non-negative integer with r<p-1. In this paper, we give a bound of the upper ramification of the torsion semi-stable representations with Hodge-Tate weights in {0,...r}. Namely, we show the upper numbering ramification group G^{(j)} (à la Fontaine) acts trivially on the p^n-torsion representations for j>u(K,r,n), where u(K,0,n)=0, u(K,1,n)=1+e(n+1/(p-1)) and u(K,r,n)=1-p^{-n}+e(n+r/(p-1)) for n>2.
	Tame characters and ramification of finite flat group schemes, J. of Number theory 128 (2008), 1091-1108 dvi, ps, pdf, abs revised on May 9, 2007
		We determine (up to $p$-power exponent) the tame characters of the semi-simplification of the Galois representation of a (commutative) finite flat group scheme $\mathcal{G}$ over the integer ring of a complete discrete valuation field of mixed characteristic by the Abbes-Saito ramification of $\mathcal{G}$. This paper contains as an appendix (and example) a determination of the Abbes-Saito conductor of the rank-one finite flat vector space schemes of Raynaud.
	Ramification and tame characters of finite flat group schemes of rank two, RIMS Kokyuroku Bessatsu 4 (2007), 153-164 abs
		This article is based on a talk at Kyoto on the paper tame characters. It contains a revised version of the preprint Hasse-Arf.
	Ramification of finite flat group schemes over local fields, J. of Number Theory 118 (2006), 145-154 abs
		We generalize Fontaine's bound of the conductor of a finite flat Galois representation of a local field to the case where the residue field may be imperfect, using the ramification theory of Abbes-Saito. We also get a slightly better bound for the $p$-power torsion subgroup of an elliptic curve with good reduction.

preprints/notes/surveys

articles in Japanese

	A classification of finite flat group schemes and framed deformations of Galois representations I pdf, abs revised on Jan. 7, 2009
		This is a note for a seminar talk I gave at Hiroshima univ. on the first two sections of M. Kisin: Moduli of finite flat group schemes, and modularity, preprint.
	Ramification theory and finite flat Galois representations pdf, abs revised on Jan. 7, 2008
		This is a note for lectures I held at Hokkaido univ. on the ramification theory of Abbes-Saito and its applications to finite flat Galois representations.
	Notes for seminars on "ARGOS seminar on intersections of modular correspondences" abs revised on Dec. 15, 2007
		These are notes (or collections of a bunch of necessary definitions and remarks) for the seminars on the article in Asterisque 312, which I held at Hokkaido university during the winter of 2007. #1: introduction and main theorems. dvi, pdf #2: supersingular elliptic curves and the representation number for quadratic forms. dvi, pdf #3: deformation theory for (one dimensional, smooth) formal groups. dvi, pdf #4: algebraic stacks and coarse moduli spaces. dvi, pdf #5: canonical and quasi-canonical liftings of height two formal groups. dvi, pdf #6: Keating's lifting theorem. dvi, pdf

teaching

	平成24年度前期: 線形代数 (経済経営学科)
	平成23年度後期: 微分積分学 (歯学部)
	平成23年度後期: 数学概論III演習
	平成23年度前期: コアセミナー
	平成22年度後期: 代数学C演習
	平成22年度後期: 数学概論III演習
	平成22年度前期: コアセミナー
	平成21年度後期: 代数学A演習
	平成21年度前期: 代数学B演習
	平成20年度後期: 解析学A演習

e-mail: shin-h____math.kyushu-u.ac.jp (replace ____ with @)
room: 501 of the Math. Bldg. in Ito Campus