A derived construction of eigenvarieties

Abstract: We construct a derived variant of Emerton's eigenvarieties using the locally analytic representation theory of p-adic groups. The main innovations include comparison and exploitation of two homotopy equivalent completed complexes associated to the locally symmetric spaces of a quasi-split reductive group 𝔾, comparison to overconvergent cohomology, proving exactness of finite slope part functor, together with some representation-theoretic statements. As a global application, we exhibit an eigenvariety coming from data of $\mathrm{GL}_n$ over a CM field as a subeigenvariety for a quasi-split unitary group.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Comments: Zoom number: 828 5069 1379

Password: 046645

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POINTS - Peking Online International Number Theory Seminar

Series comments: Description: Seminar on number theory and related topics

This seminar series is sponsored by the Beijing International Center of Mathematical Research (BICMR) and the School of Mathematical Sciences of Peking University.

The conference number and password are available on the external website. See also the announcements on bicmr.pku.edu.cn

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