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：苏 钧 博士（University of Cambridge）
题 目：Coherent cohomology of Shimura varieties I: toroidal compactifications and sheaves on them
时 间：2021.07.05（星期一），15:00-17:00
地 点：腾讯会议：558 608 783
摘 要：With modulars forms being the prototype, coherent cohomology groups of Shimura varieties make important bridges connecting Galois and automorphic representations. In non-proper cases these cohomology groups still have a nice formulation thanks to the local torus-bundle structures in Shimura varieties. Analogous to Borel and Franke’s work on cohomology of local systems on locally symmetric spaces, we establish a Hecke equivariant isomorphism between these coherent cohomology and relative Lie algebra cohomology of automorphic forms.
In this lecture we’ll embrace the construction of toroidal compactifications of Shimura varieties as well as coherent and fine sheaves on them.
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报告人：苏 钧 博士（University of Cambridge）
题 目：Coherent cohomology of Shimura varieties II: tools from analysis and automorphy
时 间：2021.07.07（星期三），15:00-17:00
地 点：腾讯会议：661 904 583
摘 要：In this lecture we’ll finish the proof (sketch) of automorphy. We’ll combine geometry of toroidal compactifications with several tools from analysis, including Dolbeault lemmas with growth control and intertwining of semigroups of operators.
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