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Seminar on Arithmetic Geometry
June 7 at 15:30 – 17:00 CEST
Minjia Zhang (Princeton University): Igusa stacks and cohomology of Shimura varieties
Shimura varieties have been playing an important role in the Langlands program. Recently, following a conjecture of Peter Scholze, we have constructed certain p-adic geometric objects, which we call ”Igusa stacks” (in the PEL type case), which encode prime-to-p information of Shimura varieties. Together with certain flag varieties (encoding information of Shimura varieties at p), they give p-adic uniformization of Shimura varieties. In this talk, I will explain construction of Igusa stack for Hodge type Shimura varieties, which leads to new proofs of Mantovan’s product formula, Eichler-Shimura relations, and vanishing type results about torsion cohomology of Shimura varieties. This is based on joint work with Patrick Daniels, Daniel Kim and Pol van Hoften.
Zoom 635 7328 0984, Kenncode: kleinste sechsstellige Primzahl