教授 (Professor)
斎藤

5. T. Saito “Ramification of local fields with

毅 (SAITO Takeshi)

imperfect residue fields III”, Mathematische Annalen, 352, Issue 3 (2012), 567-580.

A. 研究概要
正標数のスムーズな多様体上のエタール層に対6. A. Abbes and T. Saito “Ramification andし，Beilinson が特異台を余接束上に構成した．
これを使って，特性サイクルを余接束上に定義

cleanliness”, Tohoku Mathematical Journal, Centennial Issue, 63 No. 4 (2011), 775-

し，Milnor 公式，指数公式，横断的な射による853.

ひきもどしなどの性質をみたすことを証明した．

C. 口頭発表

指数公式を使って外部積との両立性と ℓ 非依存性も導いた．曲面からのプロパー射との両立性

1. The characteristic cycle and the singularも証明した．

support of an etale sheaf, Workshop ofarithmetic geometry in Tohoku, October

For an étale sheaf on a smooth variety over a30, 2014. 13:30-14:20（日本）. Arithmetic and Algebraic Geometry (Shioda75), UTokyo, School of Math. Sci., Lec-

perfect field of positive characteristic, using thesingular support recently defined by Beilinson,
I defined the characteristic cycle as a cycle onture hall, January 31, 2015, 11:20-12:20,（日本）．Séminaire Théorie des Nombres,

the cotangent bundle and proved the Milnorformula, the index formula, the compatibility

Institute de Mathématique de Bordeaux,mars 20, 2015, 14h00-15h00. Arithmetic
Algebraic Geometry, May 15, 2015, 9:30-

with the pull-back by properly transversal morphisms etc. The article on these results is submitted for publication.

10:30（中国）. Nordic Number-theory Network, Copenhagen June 16, 13:15-14:05

I proved that the characteristic cycles are compatible with exterior product and are indepen-（デンマーク）. Géométrie arithmétique,dent of ℓ, using the index formula. I also proved
the compatibility with proper push-forward formorphisms from surfaces.

théorie des représentations et applications,
24 juin 2015, 10h30-11h30（フランス）.
Guest seminar, Freie Universität Berlin,
June 30 12:30-14:00 16:00-17:30, July 2

B. 発表論文

14:15-15:45, July 7 12:00-13:00. AMS algebraic geometry summer institute, July 27,
2015, 3:20-4:10（アメリカ）. Conference on

1. T. Saito “Characteristic cycle and the Euler number of a constructible sheaf on
a surface”, Kodaira Centennial issue of
the Journal of Mathematical Sciences, theAlgebraic Number Theory, TSIMF Sanya,January 17, 2016, 9:00-10:00（中国）．

University of Tokyo, vol 22, (2015), 387442.

2. On the characteristic cycle of an l-adic
sheaf, Journees de géométrie arithmétiquede l’IHÉS 25-26 septembre 2014 IHÉS(フ2. K. Kato and T. Saito “Ramification theory for varieties over a local field,” Publi-ランス), 25 10h30-11h30, 14h00-15h00, 26

cations Mathematiques, IHES. 117, Issue
1 (2013), 1-178

10h30-11h30.
3. l 進層の分岐と特性多様体、 第三回九州合同セミナー 2014 年 1 月 11 日 佐賀大学，Characteristic cycles of a constructible

3. T. Saito “The second Stiefel-Whitneyclasses of ℓ-adic cohomology,” Journal für
die reine und angewandte Mathematik,(2013), Issue 681, 101-147.

sheaf on a surface, Arithmetic and Algebraic Geometry 2014, 東大数理大講義室
2014 年 1 月 29 日, Conference on Motivesand Galois groups on the occasion of Uwe
Jannsen’s 60th birthday, March 12 14:00-

4. T. Saito “The determinant and the discriminant of a hypersurface of even dimension,” Mathematical Research Letters. 19

15:00, 2014, University of Regensburg(ド(2012), no. 04, 855-871
1イツ). Geometry and Arithmetic of Sur-lands seminar, University of Chicago, 2012faces, March 18 10:00-11:00, 2014 LMUand TU Munich(ドイツ).

Jan. 16,D. 講義

4. The monodromy weight conjecture andperfectoid spaces (after Peter Scholze), VIASM Annual Meeting 2013, Hanoi, July

1. 数理科学基礎 (教養学部前期課程講義)：微
積分と線形代数の初歩．

20-21, 2012.（ヴェトナム）2. 微分積分学 (教養学部前期課程講義)：微積分．

5. Wild ramification and the cotangent bundle, 25/01/13 KIAS number theory sem-

3. 数学続論 XF，数物先端科学 III （数理大学院・4 年生共通講義）：エタール層の特性サ
イクル．

inar, 20/02/13 IPMU Inter-desciprinaryColloquim, 13/03/13 IHES Seminaire demathematiques, 19/03/13 ENS a Lyon,
03/07/13 AMC 2013, Busan, 24/07/13
PANT (Pan Asia Number Theory) confer-

E. 修士・博士論文
1. (博士) 寺門康裕 (TERAKADO Yasuhiro):
The determinant and the discriminant ofence, VIASM, （ヴェトナム）6. Introduction

towildramificationofa complete intersection of even dimension

schemes and sheaves, Arizona WinterSchool 2012: Ramification and Geometry
March 10-14, 2012, University of Arizona

2. (博士) 谷田川友里 (YATAGAWA Yuri):Characteristic cycle and ramification of arank 1 sheafin Tucson （アメリカ）Uni Padova March19-30, 2012

3. (修士) 清水俊也 (SHIMIZU Toshiya): 単項

7. Discriminant and determinant of a hypersurface of even dimension, 2011 年
7/27(水) 代数学コロキウム 東大数理 123

付値環における分岐理論について

F. 対外研究サービス

教室, 仙台シンポジウム 2011 年 8/2 (火)、1. 第 15, 16 回高木レクチャー 6 月 27, 28 日，
11 月 28, 29 日オーガナイザー

Une apres-midi de Geometrie Arithmetique a l’IHES 12 septembre, 2011,（フランス）2011 Japan-Taiwan Mini workshop
on Arithmetic Algebraic Geometry and re-2. 玉原数論幾何研究集会 2015，6 月 2 日 (火)–6
月 5 日 (金) オーガナイザー

lated topics, Nov. 17-19. （台湾）Number theory seminar, University of Chicago,

3. Géométrie

arithmétique,théorie

desreprésentations et applications, 22 au 26
juin 2015, Centre International de Ren-

2012 Jan. 18, Arithmetic and Algebraic
Geometry 2012 Univ. of Tokyo, 2012 Feb.
17.（日本）contres Mathématiques (CIRM), Luminy,
France. オーガナイザー

8. Second Stiefel-Whitney class of ℓ-adic cohomology, 東北大学代数幾何セミナー、

4. Documenta Mathematica, エディター

2011 年 1 月 14 日 (金) Geometrie Arithmetique et motivique, CIRM, 19 septembre 2011.（フランス）Galois Representa-

5. Japanese Journal of Mathematics, エディター

tions and Arithmetic Geometry, Institutde Mathematiques de Bordeaux, 15:1516:15, July 11 2012. Orsay, 26-03-2013,（フランス）
9. An ℓ-adic Riemann-Roch formula (jointwork with Kazuya Kato), Geometric Lang2