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： 李奇芮 博士（University of Bonn）
题 目：Double Structures and Intersection numbers in Rapoport Zink spaces
时 间：2022.04.19（星期二），15:00-17:00
地 点：腾讯会议：108-560-479
摘 要：Let K be a commutative ring with an involution σ: K—> K in the sense that σ²=id and let F be the subring of fixed points of σ in K. A double K-structure on a p-divisible group A are two ring homomorphisms K —> End(A) coincide on F. A double structure on a p-divisible group over a finite field gives rise to an intersection number in Rappoport—Zink spaces. This intersection number should be invariant under isomorphisms of double structures. A surprising fact is that this number is even invariant under isomorphisms over the algebraic closure. The identity comparing intersection numbers arises from geometrically isomorphic double structures are Guo—Jacquet’s fundamental Lemma, linear Arithmetic Fundamental Lemma, and its higher derivative generalizations. As a preparation for the next talk, we interpret Guo—Jacquet Fundamental Lemma into a comparison of intersection numbers in RZ space for étale p-divisible groups arising from two geometrically isomorphic double structures. If time allows, we formulate our general version of linear Arithmetic Fundamental Lemma for RZ spaces corresponding to basic and non-basic locus of unitary Shimura Varieties.
华罗庚青年数学论坛 学术报告2
报告人： 李奇芮 博士（University of Bonn）
题 目：Reduction formula for intersection number in RZ space
时 间：2022.04.20（星期三），15:00-17:00
地 点：腾讯会议：292-483-254
摘 要：This talk continues the discussion from our last talk. On the analytic side, there is a reduction formula reducing the value of the orbital integrals for non-elliptic orbits into a linear combination of certain products of orbital integrals for elliptic orbits, which was proved by Jiandong Guo. Our project is an arithmetic generalization for such a reduction formula. We proved a similar phenomenon for intersection numbers in certain RZ spaces as well.
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