Igusa stacks and exotic Hecke correspondences

Abstract

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.

About the Speaker

Pol van Hoften

VU Amsterdam

My name is Pol van Hoften and I'm an assistant professor (universitair docent) at VU Amsterdam.

I am interested in the Langlands programme, in particular in the mod p and p-adic geometry of Shimura varieties.

Previously I was a postdoctoral fellow at Stanford University mentored by Richard Taylor. Before that, I completed my PhD in mathematics at the London School of Geometry and Number Theory and King's College London. I was supervised by James Newton and Ana Caraiani.