p-Adic Analytic Continuation of Genus 2 Overconvergent Hilbert Eigenforms in the Inert Case

GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR
Topic:p-Adic Analytic Continuation of Genus 2 Overconvergent Hilbert Eigenforms in the Inert Case
Speaker:Yichao Tian
Affiliation:Princeton University; Member, School of Mathematics
Date:Thursday, March 17
Time/Room:2:15pm - 3:15pm/S-101

A well known result of Coleman says that p-adic overconvergent (ellitpic) eigenforms of small slope are actually classical modular forms. Now consider an overconvergent p-adic Hilbert eigenform F for a totally real field L. When p is totally split in L, Sasaki has proved a similar result on the classicality of F. In this talk, I will explain how to treat the case when L is a quadratic real field and p is inert in L.