中科院数学与系统科学研究院
数学研究所
数论研讨班
报告人：蓝凯文 教授（明尼苏达大学）
时 间：2018.12.19（星期三），09:30-10:30
题 目：Logarithmic Riemann-Hilbert correspondences for rigid varieties
摘 要：I will give an overview of the construction of a Riemann-Hilbert functor for p-adic etale local systems over smooth algebraic varieties, which can be viewed as a p-adic analogue of Deligne's classical Riemann-Hilbert correspondence for local systems over smooth algebraic varieties over the complex numbers, by establishing a logarithmic Riemann-Hilbert functor over proper smooth rigid analytic varieties. If time permits, I will try to highlight certain special phenomena which are not obvious from the outset. (This is based on joint work with Hansheng Diao, Ruochuan Liu, and Xinwen Zhu.)
时 间：2018.12.19（星期三），11:00-12:00
题 目：Local systems of Shimura varieties: a comparison of two constructions
摘 要：Given a Shimura variety, we can construct two kinds of automorphic local systems, i.e., local systems attached to algebraic representations of the associated algebraic group. The first one is based on the classical complex analytic construction using double quotients, while the second one is a p-adic analytic construction based on some recently developed p-adic analogue of the Riemann-Hilbert correspondence. I will explain how to compare these two constructions even when the Shimura variety is not of abelian type. (This is based on joint work with Hansheng Diao, Ruochuan Liu, and Xinwen Zhu.)
时 间：2018.12.21（星期五），09:30-10:30
题 目：De Rham comparison and Poincare duality for rigid varieties
摘 要：I will give an overview of the de Rham comparison isomorphisms for p-adic etale local systems over rigid varieties that are Zariski open in proper smooth rigid varieties, in the context of p-adic Riemann-Hilbert correspondences, which are compatible with the formation of cohomology with (partial) compact supports and with Poincare duality (among such cohomology). (This is joint work with Ruochuan Liu and Xinwen Zhu.)
时 间：2018.12.21（星期五），11:00-12:00
题 目：Cohomology of Shimura varieties and Hodge-Tate weights
摘 要：I will explain that the cohomology of a (general) Shimura variety with coefficients in automorphic etale local systems is de Rham with Hodge-Tate weights computable using relative Lie algebra cohomology, and that the same is true for the cohomology with compact support and the interior cohomology, and hence also for the intersection cohomology when the automorphic local systems are attached to algebraic representations of regular highest weights. (This is based on joint work with Hansheng Diao, Ruochuan Liu, and Xinwen Zhu.)
地 点：数学院南楼N817室
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