p-adic variation of motives and of automorphic forms - an introduction

Matthew Emerton

This talk will present an introduction to the philosophy of the p-adic
variation of motives, as outlined in Mazur's article "On the theme of p-adic
variation". We will discuss the relation with Iwasawa theory, and explain the
two cases where the philosophy has been developed in detail: that of motives
for GL(1) and for GL(2). In both cases, one gains crucial insight into the
situation by studying the analogous problem of p-adically interpolating
automorphic forms.