Reiner Broker<BR><BR>
 <i>p</i>-Adic class invariants<BR><BR>

<b>Abstract</b>: 
The theory of complex multiplication provides us with a means of computing a 
generating polynomial for the Hilbert class field of a given imaginary 
quadratic number field. The classical approach of using the modular j-function 
yields polynomials with huge coefficients, and as was disovered by Weber 
already, we can do better by using `smaller' functions. 

In this talk we focus on new p-adic algorithms to compute such generating 
polynomials. For the j-function this is based on a paper of Couveignes and 
Henocq, and we explain how to generalize their approach to cope with smaller 
functions over p-adic fields by using modular curves.