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

Matthew Emerton <p>

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