The aim of the course is to explain how an automorphic form can be p-adically deformed. After recalling the theory of p-adic modular forms, we shall explain the main ideas behind Hida's construction of families for ordinary forms with particular focus on the two possible different approaches (cohomological or coherent). His constructions have been generalized to many other settings (finite slope families, forms for higher rank groups) and have connections with p-adic L-functions. According to the taste of the audience we shall deal with some of these topics.
Each Tuesday-Thursday from 9 to 10 in MR11 (Pavillion B)
No class on Tue Nov 10 and Tue Dec 1. Extra class on Sat Oct 31.
References:
Diamond--Shurman, A First Course in Modular Forms, GTM 228 Springer
Hida, Elementary theory of L-functions and Eisenstein series, LMS Student Text 26, Cambridge University Press
Modular Function in one variable III, LNM 350, Springer
Calegari, Congruences between modular forms, Lecture notes for AWS 2013