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Monday, October 26, 2020
12:30 PM - 2:00 PM
Online Event

Joint Berkeley-Caltech-Stanford Number Theory Seminar

On the locally analytic vectors of the completed cohomology of modular curves
Lue Pan, Department of Mathematics, University of Chicago,

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.

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.