Companion forms and partially classical eigenvarieties

Abstract: In general, there exist $p$-adic automorphic forms of different weights with the same associated $p$-adic Galois representation. The existence of these companion forms is also predicted by Breuil's locally analytic socle conjecture in the $p$-adic local Langlands program. Under the Taylor-Wiles assumption, Breuil-Hellmann-Schraen proved the existence of all companion forms when the associated crystalline Galois representations have regular Hodge-Tate weights. In this talk, I will explain how to generalize their results to some cases when the Hodge-Tate weights are not necessarily regular. The method relies on Ding's construction of partially classical eigenvarieties and their relationships with some spaces of Galois representations.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Comments: Zoom ID: 648 9548 7663

Zoom password: 525224

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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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