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

news

	I'll be away during the following periods: May 21--28, 2023.

A list (in Japanese) of upcoming conferences of my interest is here. Conferences I (co-)organized → 等々力整数論セミナー (Todoroki Number Theory Seminar) →

publications

	[20] On a properness of the Hilbert eigenvariety at integral weights: the case of quadratic residue fields, J. Inst. Math. Jussieu 22 (2023), no. 6, 2645--2716. pdf, abs revised on Apr. 5, 2022. The final version is available here.
		Let p be a rational prime. Let F be a totally real number field which is unramified over p. Suppose that the residue degree of every prime ideal above p is 1 or 2. Then we prove the properness of the Hilbert eigenvariety at integral weights for odd p. We also prove a weaker result for p=2.
	[19] Triviality of the Hecke action on ordinary Drinfeld cuspforms of level Gamma_1(t^n), J. Reine Angew. Math 792 (2022), 269--288. pdf, abs revised on Aug. 2, 2022 (refereed version). The final version is available here
		Let k≥2 and n≥1 be any integers. In this paper, we prove that all Hecke operators act trivially on the space of ordinary Drinfeld cuspforms of level Gamma_1(t^n) and weight k.
	[18] On the compactification of the Drinfeld modular curve of level Gamma_1^Delta(n), J. of Number Theory 232 (2022), 75--100. pdf, abs revised on Jul. 16, 2020 (refereed version). The final version is available here.
		In this paper, we study the compactification of a Drinfeld modular curve of level Gamma_1(n) using Tate-Drinfeld modules in a similay way to Katz-Mazur. Previously this was the 4th section of the paper ``Duality of Drinfeld modules...''.
	[17] P-adic continuous families of Drinfeld eigenforms of finite slope, Adv. Math. 380 (2021), 107594. pdf, old, abs revised on Sep. 2, 2020 (refereed version). The final version is available here.
		Let N be a non-zero element of F_q[t] and P an irreducible polynomial dividing N. Suppose that N has a prime factor of degree one. In this paper, we construct families of Drinfeld cuspidal eigenforms of level Gamma_1(N) in which Hecke eigenvalues vary in a P-adically continuous way.
	[16] Dimension variation of Gouvêa-Mazur type for Drinfeld cuspforms of level Gamma_1(t), Int. Math. Res. Not. 2021 (2021), no. 3, 2389--2402. pdf, slide, abs revised on Apr. 25, 2019. The final version is available here.
		In this paper, we prove an analogue of the Gouvêa-Mazur conjecture for Drinfeld cuspforms of level Gamma_1(t).
	[15] Duality of Drinfeld modules and P-adic properties of Drinfeld modular forms, J. Lond. Math. Soc. 103 (2021), no. 1, 35--70. pdf, old, abs revised on Jul. 18, 2020 (refereed version). The final version is available here.
		Let p be a rational prime, q a p-power and A=F_q[t]. Let P be a monic irreducible polynomial in A. In this paper, we develop a geometric theory of P-adic Drinfeld modular forms a la Katz, using the duality theory of Taguchi.
	[14] Irreducible components of the eigencurve of finite degree are finite over the weight space (with James Newton), J. Reine Angew. Math. 763 (2020), 251--269. pdf, abs revised on Aug. 1, 2018 (refereed version). The final version is available here.
		In this paper, we prove that any irreducible component of the Coleman-Mazur eigencurve of tame level N which is of finite degree over the weight space is in fact finite over the weight space. Combined with an argument of Chenevier and a conjecture of Buzzard-Kilford (which has been proven in special cases, and for general quaternionic eigencurves) this shows that the only finite degree components of the eigencurve are the ordinary components.
	[13] Integral p-adic Hodge theory and ramification of crystalline representations, Panor. Synthèses 54 (2019), 159--203. pdf, old, abs revised on May 9, 2019 (final version)
		These are notes on integral p-adic Hodge theory as of 2014 (especially on the Fontaine-Laffaille theory) and the classical ramification bound of torsion crystalline representations due to Abrashkin-Fontaine, based on my talks at the spring school "Classical and p-adic Hodge theories". The previous title is "Ramification of crystalline representations" which I changed following the referee's suggestion.
	[12] On canonical subgroups of Hilbert-Blumenthal abelian varieties, J. Théor. Nombres Bordeaux 30 (2018), no. 2, 355--391. pdf, abs revised on Apr. 8, 2017 (refereed version). The final version is available here.
		Let p be a rational prime. Let F be a totally real number field which is unramified over p. In this paper, we present a theory of canonical subgroups for Hilbert-Blumenthal abelian varieties with O_F action, which is used in the paper ``On a properness of the Hilbert eigenvariety...''. This is §3 of an old version of that paper.
	[11] Ramification theory and perfectoid spaces -- a survey, RIMS Kokyuroku Bessatsu 53 (2015), 47--63. pdf, abs revised on Oct. 6, 2014 (refereed version)
		This is a survey article for the paper ``Ramification theory and perfectoid spaces'', based on my talk at RIMS.
	[10] On lower ramification subgroups and canonical subgroups, Algebra & Number Theory 8 (2014), 303--330. pdf, abs revised on Nov. 18, 2012 (refereed version). The final version is available here.
		In this paper, we generalize the main theorem of the article "Ramification correspondence..." to the case of p=2. Moreover, we also prove that the higher canonical subgroups constructed in the article "Canonical subgroups via Breuil-Kisin modules" and "...for p=2" appear in the lower ramification filtration.
	[9] Ramification theory and perfectoid spaces, Compos. Math. 150 (2014), 798--834. pdf, old, abs revised on Sep 28, 2013. These pdf files are different from the final publication available here.
		In this paper, we prove various correspondence results of ramification of finite extensions of complete discrete valuation fields of residue characteristic p>0, using the theory of perfectoid spaces.
	[8] Canonical subgroups via Breuil-Kisin modules for p=2, J. of Number Theory 137 (2014), 142--159. pdf, old2, old, abs revised on Nov. 5, 2013 (refereed version). The final version is available at ScienceDirect.
		In this article, we generalize the results in the paper ``Canonical subgroups via Breuil-Kisin modules'' to the case of p=2, using Kisin's classification of connected finite flat group schemes.
	[7] Canonical subgroups via Breuil-Kisin modules, Math. Z. 274 (2013), 933--953. pdf, abs, errata revised on Oct. 3, 2012 (refereed version). The final version is available here.
		Let p>2 be a rational prime and K/Q_p be an extension of complete discrete valuation fields. Let G be a truncated Barsotti-Tate group of level n, height h and dimension d over O_K with 0<d<h. In this paper, we construct a finite flat closed subgroup scheme of G which lifts the Frobenius kernel of a reduction of G, if the Hodge height of G is less than 1/(p^{n-2}(p+1)). We also prove the usual properties as the canonical subgroup (degree of the quotient, freeness, Hodge-Tate kernel, coincidence with a ramification subgroup, a control on anti-canonical isogenies, uniqueness, family) under conditions on the Hodge height.
	[6] Ramification correspondence of finite flat group schemes over equal and mixed characteristic local fields, J. of Number Theory 132 (2012), 2084--2102. pdf, old2, old, abs revised on Feb. 14, 2012 (refereed version). The final version is available here.
		Let p>2 be a rational prime, k be a perfect field of characteristic p and K be a totally ramified extension of Frac(W(k)). Let G and H be finite flat group schemes killed by p over O_K and k[[u]], respectively. In this paper, we show the upper ramification subgroups in the sense of Abbes-Saito of G and H is naturally isomorphic to each other when they are associated to the same Kisin module. This can be viewed as a geometric aspect of the functor of norm fields and enable us to reduce the study of ramification of a finite flat group scheme over O_K killed by p to the case where the base is the equal characteristic complete discrete valuation ring k[[u]].
	[5] Ramification correspondence of finite flat group schemes and canonical subgroups -- a survey, RIMS Kokyuroku Bessatsu 32 (2012), 3--18. pdf, abs revised on Mar. 28, 2011
		This is a peer-reviewed survey of the papers ``Ramification correspondence'' and ``Canonical subgroups'', as of March 2011.
	[4] On a ramification bound of torsion semi-stable representations over a local field, J. of Number theory 129 (2009), 2474--2503. abs The final version is available here.
		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.
	[3] 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. The final version is available here.
		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 G over the integer ring of a complete discrete valuation field of mixed characteristic by the Abbes-Saito ramification of 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.
	[2] 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.
	[1] Ramification of finite flat group schemes over a local field, J. of Number Theory 118 (2006), 145--154. abs, errata The final version is available here.
		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.

notes/unpublished articles

articles in Japanese

	Drinfeld加群の双対性とP進Drinfeld保型形式, 第11回福岡数論研究集会報告集. pdf, abs revised on Sep. 28, 2017
		These are notes for my talk at 11th Fukuoka Symposium on Number Theory on the paper "Duality of Drinfeld modules...".
	Coleman-Mazur固有値曲線の次数有限な既約成分は重さ空間上有限, 2017早稲田整数論研究集会報告集. pdf, abs revised on Jun. 22, 2017
		These are notes for my talk at Waseda Number Theory Symposium 2017 on the paper "Irreducible components of the eigencurve...".
	アーベル多様体の標準部分群とヒルベルト固有値多様体, 第61回代数学シンポジウム報告集. pdf, abs revised on Dec. 31, 2016
		These are notes for my talk at Algebra Symposium 2016 on the paper "On a properness of the Hilbert eigenvariety...".
	有限平坦群スキームの分類とガロア表現の枠付き変形I pdf, abs revised on Jan. 7, 2009
		These are notes 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.
	分岐理論と有限平坦Galois 表現 pdf, abs revised on Jan. 7, 2008
		These are notes 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30年度～現在（東京都市大学）→
	平成20～29年度（九州大学）→

e-mail: hattoris____tcu.ac.jp (replace ____ with @) このメールアドレスへの特定電子メールの送信を拒否します．