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BIMSA-YMSC Tsinghua Number Theory Seminar
Langlands-Kottwitz method for the bad reduction of simple Shimura varieties
Langlands-Kottwitz method for the bad reduction of simple Shimura varieties
Organizers
Hansheng Diao
, Yueke Hu
, Emmanuel Lecouturier
,
Cezar Lupu
Speaker
Jingren Chi
Time
Monday, May 6, 2024 10:00 AM - 11:00 AM
Venue
Shuangqing-B627
Abstract
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.