|Date: Monday, December 04, 2017
Location: 4088 East Hall (4:10 PM to 5:30 PM)
Title: Critical p-adic L-functions for Hilbert modular forms
Abstract: Shimura proved that the L-function for a Hilbert modular form has certain critical values which are algebraic after normalization by periods. A p-adic L-function is meant to interpolate these critical values. Together with a certain growth condition, it is uniquely determined by the interpolation property in the so-called small slope case (modulo Leopoldt's conjecture). For this reason, the constructions tend to be limited to this case in general. For usual modular forms, i.e. over Q, the small slope restriction in the constructions was removed by Pollack-Stevens and Bellaiche. In this talk I will explain how to move beyond small slope cases for general totally real fields. The main tool is a p-adic family of Hilbert modular forms, which allows us to degenerate to large slope cases from small slope cases. The main technical result we need is a smoothness statement for the family. Its role is to guarantee that our degeneration is essentially unique (a p-adic multiplicity one statement). This is all joint work with David Hansen.
Speaker: John Bergdall
Institution: Michigan State University
Event Organizer: Kartik Prasanna