Some Vanishing Results for Rational Completed Cohomology of Shimura Varieties

Explore the concept of p-adically completed cohomology in Shimura varieties through this 1-hour 6-minute lecture. Delve into Emerton's introduction of p-adically completed cohomology as a representation of p-adic groups and its interpretation as spaces of p-adic automorphic forms. Examine the speaker's explanation of how sufficiently regular infinitesimal characters of the p-adic group can only appear in the middle degree of completed cohomology for Shimura varieties. Gain insights into the proof methodology, which combines Bhatt's recent findings on Kodaira vanishing in mixed characteristic with established techniques involving translation functors. Enhance your understanding of advanced mathematical concepts in algebraic geometry and number theory through this in-depth presentation at the Hausdorff Center for Mathematics.