GLNT: Higher p-adic modular forms; Frobenius lifting and a geometric theory of companion forms

George Boxer's talk:
Title: Higher p-adic modular forms

Abstract: The goal of the theory of higher p-adic modular forms is to study the p-adic properties of higher coherent cohomology of Shimura varieties, just as usual p-adic modular forms are used to study classical modular forms (or coherent H^0). In this talk I will try to motivate why we should study higher coherent cohomology of Shimura varieties and then give an introduction to higher p-adic modular forms and in particular some generalizations of the works of Hida and Coleman on classicality and families. All this is joint with Vincent Pilloni.

Vincent Pilloni's talk:
Title : Frobenius lifting and a geometric theory of companion forms

Abstract : We describe the obstruction to lift Frobenius on Siegel Shimura varieties modulo p^2. We give an application to the theory of companion forms on the modular curve (originally due to Gross, Coleman-Voloch, Faltings-Jordan) and on Siegel threefolds.