Some vanishing results for the rational completed cohomology of Shimura varieties

Abstract: I will start with some introduction to Shimura varieties and their completed cohomology, and report on my joint work in progress with Lue Pan which shows that, in the rational p-adic completed cohomology of a general Shimura variety, "sufficiently regular" infinitesimal weights (whose meaning will be explained) can only show up in the middle degree. I will give some examples and explain the main ingredients in our work, if time permits.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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