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

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.

Research Interest:

Arithmetic Geometry, Automorphic Representations, Geometric Representation Theory

Personal homepage:

http://www.mcm.ac.cn/people/members/202108/t20210823_658347.html