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Langlands-Kottwitz method for the bad reduction of simple Shimura varieties

组织者

刁晗生 , 胡悦科 , 埃马纽埃尔·勒库图里耶 , 凯撒·鲁普

演讲者

迟敬人

时间

2024年05月06日 10:00 至 11:00

地点

Shuangqing-B627

摘要

In this talk we first introduce the attempts of Rapoport, Scholze and Scholze-Shin to extend the Langlands-Kottwitz method of describing etale cohomology of Shimura varieties to cases of bad reduction (in which the level structure could be arbitrary and the local group could be non-quasi-split). In their approach, the problem is reduced to certain conjectures on orbital integrals and characters of local test functions that are of independent interest. Then I will explain some progress on these conjectures for inner forms of $GL(n)$. This is based on joint work with Thomas Haines.