【开课说明】

举办日期：2021年11月29日 12月06日 16:00 - 18:00   12月02/09/13/16日 15:00 - 17:00

举办地点：线上课程（Zoom Meeting）

会议ID：  561 420 9883 密码：20211129  

授课导师：余家富 教授 中研院数学所

主办单位：国家天元数学中部中心、武汉大学数学与统计学院

课时数：18 课时

【课程摘要】

    The moduli spaces of polarized abelian varieties have been playing an important role and have been intensively investigated in the modern theory of arithmetic geometry. The purpose of this short course is to introduce the geometry of Siegel modular varieties modulo a prime p. This topic contains many deep results and we limit ourselves to the EO(Ekedahl-Oort) stratification, especially combinatorial and group-theoretic descriptions, its relation with Newton stratification and KR(Kottwitz-Rapoport) stratification in lower dimensions (say g<=3), as well as the connection with Deligne-Lusztig varieties. For them we will also introduce necessary basics and background in the theory of reductive groups and Dieudonne modules.

Prerequisites: notion of schemes or algebraic varieties and basics in abelian varieties and algebraic groups.

References:

[GH] U. Goertz and Hoeve, Ekedahl-Oort strata and Kottwitz-Rapoport strata. J. Algebra 351 (2012), 160--174.

[Har] S. Harashita, Ekedahl-Oort strata contained in the supersingular locus and Deligne-Lusztig varieties. J. Alg. Geom. 19 (2010), no. 3, 419--438.

[Hart] P. Hartwig On the reduction of the Siegel moduli space of abelian varieties of dimension 3 with Iwahori level structure. Muenster J. Math. 4 (2011), 185--226.

[O] F. Oort, A stratification of a moduli space of abelian varieties. Moduli of Abelian Varieties, 345—416, 2001.

[Y] C.-F. Yu Kottwitz-Rapoport strata in the Siegel moduli spaces. Taiwanese J. Math. 14 (2010), no. 6, 2343--2364.

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