[Japanese / English]

Designated Assistant Professor at Graduate School of Mathematics, Nagoya University (2016/05 –)

*Wild automorphisms on K3 surfaces in mixed characteristic*, in preparation.*μ_n-actions on K3 surfaces in positive characteristic*, preprint arXiv:1710.07158 new! [poster for Kinosaki symposium]- with Hisanori Ohashi and Sławomir Rams,
*On automorphisms of Enriques surfaces and their entropy*, preprint arXiv:1707.02563 *Degeneration of K3 surfaces with non-symplectic automorphisms*, preprint arXiv:1612.07569.*Extendability of automorphisms of K3 surfaces*, preprint arXiv:1611.02092.- with Christian Liedtke,
*Good reduction of K3 surfaces*, Compositio Math. 154 (2018), 1–35. (arXiv:1411.4797v3) *Good reduction criterion for K3 surfaces: an announcement*(in Japanese), Algebraic Number Theory and Related Topics 2013, RIMS Kôkyûroku Bessatsu B44 (2013), 95–102.*Good reduction criterion for K3 surfaces*, Mathematische Zeitschrift 279 (2015), no. 1–2, 241–266. (arXiv:1401.1261)*On good reduction of some K3 surfaces related to abelian surfaces*, Tohoku Math. J. (2) 67 (2015), no. 1, 83–104. (arXiv:1202.2421)*On good reduction of some K3 surfaces (announcement)*(in Japanese), Algebraic Number Theory and Related Topics 2011, RIMS Kôkyûroku Bessatsu B44 (2013), 111–113.

*Good reduction criterion for K3 surfaces*, in proceedings of Kinosaki symposium on algebraic geometry 2014 (published 2015), 80–87. (non-refereed)*志村多様体と K3 曲面：Tate 予想への応用*[survey] (in Japanese) in proceedings of Number Theory Summer school 2015, in preparation, current manuscript (2016/07/31)

- μ_n-actions on K3 surfaces in positive characteristic, 正標数の代数幾何とその関連する話題, 法政大学小金井キャンパス西館６階6010号室, 2018/01/30 - 02/01.
- μ_p- and α_p-actions on K3 surfaces in characteristic p, K3 surfaces and related topics, Nagoya University, 2017/12/19.

- μ_n-actions on K3 surfaces in positive characteristic, Arithmetic Geometry and Related Topics, Ehime University, 2017/11/20.
- μ_n-actions on K3 surfaces in positive characteristic, p進コホモロジーと数論幾何学2, Tokyo Denki University, 2017/11/17.
- μ_n-actions on K3 surfaces in positive characteristic, Algebraic Geometry Seminar, Nagoya University, 2017/10/30.
- μ_n-actions on K3 surfaces in positive characteristic [poster], Kinosaki symposium on algebraic geometry 2017, Kinosaki International Arts Center, 2017/10/23-27.
- μ_p-quotients of K3 surfaces in characteristic p (in Japanese), 第５回 K3曲面・エンリケス曲面ワークショップ, Hokkaido University of Education, 2017/08/24.
- μ_p-quotients of K3 surfaces in characteristic p (in Japanese), Algebraic Geometry Seminar, Tokyo University of Science, 2017/08/02 15:00.
- Wild automorphisms on K3 surfaces in mixed characteristic, Algebraic Geometry Seminar, Nagoya University, 2017/06/05.
- Wild automorphisms on K3 surfaces in mixed characteristic, Hakodate workshop on arithmetic geometry 2017, Hakodate Hokuyo building, 2017/05/30.
- Degeneration of K3 surfaces and automorphisms, Number Theory Seminar, Osaka University, 2017/05/26.
- Degeneration of K3 surfaces and automorphisms, 野田代数幾何学シンポジウム, Tokyo University of Science, 2017/03/23.
- Degeneration of K3 surfaces and automorphisms, [video], New Trends in Arithmetic and Geometry of Algebraic Surfaces, Banff International Research Station, Banff, Canada, 2017/03/13.
- Degeneration of K3 surfaces and automorphisms, 数論幾何研究報告会, The University of Tokyo, 2017/03/09.
- Degeneration of K3 surfaces and automorphisms, Workshop on Fano varieties and Calabi-Yau varieties, Kobe University, 2017/01/24.
- Degeneration of K3 surfaces and automorphisms, Workshop on Shimura varieties, representation theory and related topics, Kyoto University, 2016/11/25.
- The Tate conjecture for K3 surfaces over finite fields [survey] (in Japanese), Algebraic Geometry Seminar, Nagoya University, 2016/10/24.
- Extendability of automorphisms of K3 surfaces (in Japanese), Algebraic Geometry Seminar, Kyoto University, 2016/10/14.
- Extendability of automorphisms of K3 surfaces (in Japanese), Workshop on arithmetic geometry at Tambara 2016, Tambara Institute of Mathematical Sciences, The University of Tokyo, 2016/06/21.
- Extendability of automorphisms of K3 surfaces (in Japanese), Algebraic Geometry Seminar, Nagoya University, 2016/05/30.
- Good reduction of K3 surfaces (in Japanese), Algebraic Geometry Seminar, Nagoya University, 2016/05/16.
- Extendability of automorphisms of K3 surfaces, Séminaire de théorie des nombres de l'IMJ-PRG, Jussieu, Paris, France, 2016/03/14.
- Good reduction of K3 surfaces, Conference on K3 surfaces and related topics, KIAS, Seoul, Korea, 2015/11/18.
- 志村多様体と K3 曲面：Tate 予想への応用 [survey] (in Japanese), 2015 年度整数論サマースクール 「志村多様体とその応用」, 南田温泉ホテルアップルランド, 2015/08/19.
- Good reduction of K3 surfaces,
Algebraic Geometry Seminar,
University of Tokyo,
2015/05/25.
<abstract>

We consider degeneration of K3 surfaces over a 1-dimensional base scheme of mixed characteristic (e.g. Spec of the p-adic integers). Under the assumption of potential semistable reduction, we first prove that a trivial monodromy action on the l-adic etale cohomology group implies potential good reduction, where potential means that we allow a finite base extension. Moreover we show that a finite etale base change suffices. The proof for the first part involves a mixed characteristic 3-dimensional MMP (Kawamata) and the classification of semistable degeneration of K3 surfaces (Kulikov, Persson--Pinkham, Nakkajima). For the second part, we consider flops and descent arguments. This is a joint work with Christian Liedtke. - Good reduction of K3 surfaces (in Japanese), algebra seminar, Tokyo Institute of Technology, 2014/12/10.
- Good reduction criterion for K3 surfaces, Kinosaki symposium on algebraic geometry 2014, Kinosaki conference hall, 2014/10/23.
- Good reduction criterion for K3 surfaces (in Japanese), Workshop on K3 surfaces and Enriques surfaces, Asahikawa, 2014/09/01.
- Good reduction criterion for K3 surfaces, seminar (Arbeitsgemeinschaft Algebra), Technische Universität München, 2014/06/24.
- Good reduction criterion for K3 surfaces (in Japanese), Algebraic Number Theory and Related Topics 2013, RIMS, Kyoto University, 2013/12/13.
- Good reduction criterion for K3 surfaces (in Japanese), seminar at Kyoto University, 2013/11/01.
- Good reduction criterion for K3 surfaces (in Japanese),
Algebra seminar,
Tohoku University,
2013/10/24.
<abstract> (for the three talks above)

The Néron-Ogg-Shafarevich criterion states that an abelian variety (over a complete discrete valuation field) has good reduction if and only if the Galois action on the ($l$-adic) Tate module satisfies a certain property. In the complex case, there is a similar criterion for K3 surfaces, which can be deduced from a result of Kulikov on semistable reduction of complex K3 surfaces. In this talk we show a similar criterion for K3 surfaces (using the $l$-adic cohomology in place of the $l$-adic Tate module) in the mixed characteristic case. - Good reduction criterion for K3 surfaces (in Japanese),
Hiroshima Workshop on Number Theory,
Hiroshima University,
2013/07/16.
<abstract>

The Néron–Ogg–Shafarevich criterion states that an abelian variety over a CDVF has good reduction if and only if the Galois action on the ($l$-adic) Tate module satisfies a certain property. We show that a similar criterion holds for good reduction of K3 surfaces (using the $l$-adic étale cohomology in place of the $l$-adic Tate module). We also give examples which indicate that the situation is not completely parallel between these (K3 and abelian) cases. - Good reduction criterion for K3 surfaces,
Workshop on the arithmetic geometry of Shimura varieties, representation theory, and related topics,
Hokkaido University,
2012/07/19.
<abstract>

Abelian varieties over local fields have good reduction if and only if their $l$-adic etale cohomology (equivalently Tate modules) are unramified [Serre–Tate]. I prove a similar result for (potential) good reduction of projective K3 surfaces of small degree (relative to the residue characteristic). This result covers wider classes of K3 surfaces than those in my previous talks (in Kyoto, Hiroshima, Kyushu). - On good reduction of some K3 surfaces [poster session], Arithmetic Geometry Week in Tokyo, University of Tokyo, 2012/06/04–08.
- On good reduction of some K3 surfaces (in Japanese), Kyushu Algebraic Number Theory 2012, Kyushu University, 2012/02/23.
- On good reduction of some K3 surfaces (in Japanese), Algebraic Number Theory and Related Topics, RIMS, Kyoto University, 2011/12/02.
- On good reduction of some K3 surfaces (in Japanese),
Hiroshima Workshop on Number Theory,
Hiroshima University,
2011/07/21.
<abstract>

Let $X$ be a variety over a local field $K$.

If $X$ is an abelian variety, a theorem of Serre–Tate shows that $X$ has good reduction if and only if its $l$-adic etale cohomology is unramified (a Galois representation of $K$ is unramified if the action of the inertia group is trivial).

In this talk, I prove that similar results holds if $X$ belongs to certain classes of K3 surfaces. - On good reduction of some K3 surfaces,
Workshop on the arithmetic geometry of Shimura varieties and Rapoport-Zink spaces,
Kyoto University,
2011/07/06.
<abstract>

same as above. - On good reduction of some K3 surfaces (in Japanese), Number Theory Seminar, University of Tokyo, 2011/05/25.

singular fibers of elliptic surfaces (DVI) (2011/06/02):
mainly for personal use. Now covers types I_{0}*, IV*, and II*.

Paris memo (2015/11/01): written in Japanese/French. No longer maintained.

(There are some other pages written only in Japanese. )

last modified: 2017/12/11

page admin: Yuya MATSUMOTO

(matsumoto.yuya AT math.nagoya-u.ac.jp)