中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
华罗庚青年数学论坛
学术报告
报告人： Prof. Rong Zhou（University of Cambridge）
题 目：Independence of l for Frobenius conjugacy class attached to abelian varieties
时 间：2021.12.09（星期四），09:00-10:00
地 点：Zoom会议：412 019 4771 密码：mcm1234
摘 要：Let A be an abelian variety over a number field E and let G denote the Mumford–Tate group ofA. After replacing E by a finite extension, the action of the absolute Galois group of E on the l-adic cohomology H1_et(A,Ql)factors through G(Ql).We show that for p an odd prime and v|p a place of E where A has good reduction, the conjugacy class of Frobenius Frobv in G(Ql)is independent of l. A key input for our approach is to study families of abelian varieties whose Mumford-Tate groups are contained in G, and especially the structure of their mod p reductions. This is joint work with M. Kisin.
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报告人： Prof. Rong Zhou（University of Cambridge）
题 目：Components in the basic locus of Shimura varieties
时 间：2021.12.10（星期五），09:00-10:00
地 点：Zoom会议：412 019 4771 密码：mcm1234
摘 要：The basic locus of Shimura varieties is the generalization of the supersingular locus in themodular curve and provides us with an interesting class of cycles in the special fiber of Shimura varieties. In this talk, we give a description of the set of irreducible components in the basic locus of Hodge type Shimura varieties in terms of class setsfor an inner form of the structure group, generalizing a classical result of Deuring and Serre. A key input for our approach is an analysis of certain twisted orbital integrals using techniques from local harmonic analysis in order to understand the geometryof affine Deligne-Lusztig varieties. The result for the basic locus is then deduced from this using the Rapoport-Zink uniformization. This is joint work with X. He and Y. Zhu.
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