Title I: Igusa stacks and exotic Hecke correspondences I

Abstract: Igusa stacks are conjectural p-adic analytic objects related to Shimura varieties, which were conjectured to exist by Scholze. In this talk I aim to give motivation for this conjecture, as well as a review of some of the objects involved. I will then discuss my joint work with Patrick Daniels, Dongryul Kim and Mingjia Zhang (张明嘉) in which we prove the conjecture for Shimura varieties of Hodge type (this extends the PhD thesis of Mingjia Zhang which deals with the case of PEL type AC Shimura varieties).

Title II: Igusa stacks and exotic Hecke correspondences II

Abstract: In this talk, I will discuss cohomological consequences of the existence of Igusa stacks, such as torsion vanishing results. Additionally, I will explain some of the ideas of the proofs of the existence of Igusa stacks.

*The whole lecture series has four lectures, and the later two will be in MCM.

Videos:  http://archive.ymsc.tsinghua.edu.cn/pacm_course?html=Igusa_stacks_and_exotic_Hecke_correspondences.html