Correspondences between mod p fiber of Shimura varieties

Correspondences between mod p fiber of Shimura varieties

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Xinwen Zhu, Minerva Distinguished Visitor
Fine Hall 314

Abstract: Moduli of local Shtukas controls mod p geometry of Shimura varieties. I will discuss how categorical trace of geometric Satake allows one to construct Hecke-equivariant maps before cohomology of (different) Shimura varieties. A consequence of this construction is the Tate conjecture of mod p fibers of Shimura varieties in generic cases.