Event Type
Seminar
Monday, October 26, 2020 12:30 PM
Lue Pan (University of Chicago)

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.