On the locally analytic vectors of the completed cohomology of modular curves
Lue Pan (University of Chicago)
24-Nov-2020, 21:30-22:30 (3 years ago)
Abstract: A classical result identifies holomorphic modular forms with highest weight vectors of certain representations of $SL_2(\mathbb{R})$. We study locally analytic vectors of the (p-adically) completed cohomology of modular curves and prove a p-adic analogue of this result. As applications, we are able to prove a classicality result for overconvergent eigenforms and give a new proof of Fontaine-Mazur conjecture in the irregular case under some mild hypothesis. One technical tool is relative Sen theory which allows us to relate infinitesimal group action with Hodge(-Tate) structure.
algebraic geometrynumber theory
Audience: researchers in the topic
Series comments: To receive announcements by email, add yourself to the nt mailing list.
Organizers: | Edgar Costa*, Siyan Daniel Li-Huerta*, Bjorn Poonen*, David Roe*, Andrew Sutherland*, Robin Zhang*, Wei Zhang*, Shiva Chidambaram* |
*contact for this listing |
Export talk to