教授 (Professor)

lois representations”, Nagoya Mathemati-

斎藤

cal Journal 236 (2019), 134–182.

毅 (SAITO Takeshi)

4. T. Saito “Ramiﬁcation groups of coverings

A. 研究概要

and valuations”, Tunisian Journal of Math-

剰余体が一般の局所体の分岐群の部分商について

ematics Vol. 1, No. 3, 373-426, 2019

特性形式が定義できたことでこの理論の基礎が一

5. T. Saito “On the proper push-forward of

段落ついたので，分岐群とその幾何的応用についthe characteristic cycle of a constructibleての本の原稿を書き始め，これまでに 300 ページ

sheaf”, Proceedings of Symposia in Pure

弱できた．その中で，局所体上の曲線上のエター

Mathematics Volume: 97; 2018; Algebraic

ル層の隣接輪体の次元公式の曲線のコンパクト化

Geometry: Salt Lake City 2015, Part 2,をしない新しい証明を得た．

485-494

去年投稿した Frobenius–Witt 微分，混標数のス

6. T. Saito, Y. Yatagawa “Wild ramiﬁcation

キーム上のエタール層の特異台，分岐群の次数商

determines the characteristic cycle”, An-についての論文のレフェリーレポートが来たので

nales Scientiﬁques de l’Ecole normale su-

改訂した．初めの 2 つは掲載が決定している．

perieure, 50, fascicule 4 (2017), 1065-1079.
7. T. Saito “Characteristic cycle of the ex-

The foundation on the ramiﬁcation groups ofternal product of constructible sheaves”,

local ﬁelds with imperfect residue ﬁelds was laid

Manuscripta Mathematica, 154, Issue 1-2,

last year by the deﬁnition of the characteristic

2017, pp 1-12.

forms on the graded quotients. I started writ-8. T. Saito “Wild ramiﬁcation and the cotan-

ing a book on the theory and geometric applica-gent bundle”, Journal of Algebraic Geom-

tions and nearly 300 pages are already written.

etry, 26 (2017), 399-473.

On writing, I ﬁnd a new proof of the dimen-

9. T. Saito “The characteristic cycle and thesion formula for nearby cycles of étale sheaves

singular support of a constructible sheaf”,

on curves over a local ﬁeld without using com-

Inventiones mathematicae, 207(2), (2017)

pactiﬁcation of the curve.

597-695,

I received referee reports on the three articles
submitted last year on Frobenius–Witt diﬀer-C. 口頭発表

entials, singular supports of étale sheaves on

1. Micro support of a constructible sheaf inschemes of mixed characteristic and the graded

mixed characteristic, Conference en hon-quotients of ramiﬁcation groups and revised

neur de Luc Illusie , June 8, 2021. （フthem. The ﬁrst two are accepted for publica-ランス online）

tion.

2. Wild ramiﬁcation and the cotangent bun-B. 発表論文

dle in mixed characteristic Eighth Paciﬁc

1. T. Saito “Characteristic cycles and the con-

Rim Conference 7 August, 2020 （アメリカ

ductor of direct image”, Journal of theonline）Colloquium at University of Mine-

American Mathematical Society 34 (2021),sota, Feb 18, 2021.
3. Graded Quotients of Ramiﬁcation Groups

369–410
ofof a Local Field with Imperfect Residue

two Swan conductors of abelian charac-Field, January 7, 2020, Internationalters”, Épijournal de Géométrie Algébrique,conference on arithmetic geometry 2020,epiga:5395, 11 novembre 2019, Volume 3

TIFR, Mumbai.（インド）mercredi 22 janv.

2. K.

Kato,T.

Saito“Coincidence2020, IHES.（フランス）

3. K. Kato, I. Leal, T. Saito “Reﬁned Swan

4. Etale Cohomology and the Characteristic

conductors mod p of one-dimensional Ga-1

Cycle, September 6, 2019, BICMR, Pekinhonor of Masaki Kashiwara’s 70th birth-

University. （中国）

day IHES, June 9 2017（フランス）. Al-5. Ramiﬁcation groups of a local ﬁeld (withgebraic Analysis and Representation The-

Ahmed Abbes and Kazuya Kato), Septem-

ory – In honor of Professor Masaki Kashi-

ber 5, 2019 CAS Beijing.（中国）wara’s 70th Birthday – RIMS June 28 （日6. CC, Wild Ramiﬁcation and Irregular Sin-

本）. Regulators in Niseko 2017, 2017 年 9gularities, Sep 25, 2019 at IMPAN in War-

月 4 日. Tokyo-Lyon Satellite Conference insaw, Poland.（ポーランド）

Number Theory, Univ. of Tokyo, February

7. Characteristic cycle of a constructible

21 (Wed), 2018. 第 34 回京都賞記念ワーク

sheaf, Arithmetic Geometry in Carthage,

ショップ「基礎科学部門」2018 年 11 月 12Summer School, Tunisian Academy Beit al-日（月）京大数理研 Arithmetic and Alge-Hikma, Carthage, Tunisia Thursday, Junebraic Geometry 2019 - in honour of Pro-

20-21, 2019.（チュニジア）fessor Tomohide Terasoma’s 60th birthday

8. Characteristic

cycleof- January 25 (Fri), 2019 東大数理，CASconstructible

Beijing, September 4, 2019（中国）sheaves and restriction to curves. "Arithmétique et géométrie algébrique", une

E. 修士・博士論文

conférence en l’honneur d’Ofer Gabber, à1. (修士) 松田 光智 (MATSUDA Koji): Tor-l’occasion de son soixantième anniversaire,à l’IHÉS, Vendredi 15 juin, 2018.（ フ ラsion points of elliptic curves over multi-ン ス ）Cohomology of algebraic varieties

quadratic ﬁelds and cyclotomic ﬁelds

CIRM October 19th, 2018. （フランス）

F. 対外研究サービス

9. Characteristic cycles and the conductor of

1. Tokyo–Berkeley Workshop on Number

direct image, Interactions between Repre-

Theory March 14-17, online オーガナイザー

sentation Theory and Algebraic Geome-

2. Journal of Algebraic Geometry, エディター

try, the University of Chicago, August 22,

3. Documenta Mathematica, エディター

2017 （アメリカ）, p 進コホモロジーと数

4. Japanese Journal of Mathematics, エディ

論幾何学， 東京電機大学 11 月 16 日, Theター

Legacy of Carl Friedrich Gauss, Dec 18,
2017, TSIMF, Sanya, （中国）. Motives
in Tokyo on the occation of Shuji Saito’s
60th Birthday March 26, 2018, Univ. ofTokyo.
10. Characteristic cycle of an ℓ-adic sheaf, 東
北 大 学 代 数 セ ミ ナ ー 2017 年 1 月 26 日 ，第 12 回 鹿児島 代数・解析・幾何学セミ
ナー 2017 年 2 月 13 日，JAMI 2017 Local

zeta functions and the arithmetic of moduli
spaces: A conference in memory of JunIchi Igusa March 22-26, 2017 Johns Hopkins University（アメリカ）, Fukuoka International Conference on Arithmetic Geometry in 2017 April 20, (日本). Workshop
on arithmetic geometry at Tambara 2017
May 22, （日本）. Algebraic Analysis in2