Regular de Rham Galois representations in the completed cohomology of modular curves

Abstract: Let $p$ be a prime. I want to explain how to use the geometry of modular curves at infinite level and Hodge-Tate period map to study $p$-adic regular de Rham Galois representations appearing in the $p$-adically completed cohomology of modular curves. We will show that these Galois representations up to twists come from modular forms and give a geometric description of the locally analytic representations of $\mathrm{GL}_2(\mathbb{Q}_p)$ associated to them. These results were previously known by totally different methods.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Comments: Zoom ID = 953 6788 4415

Zoom password = 373352

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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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