X

FOREWORD

GL2, which constructs systems of/-adic representations whose L-series is a given

automorphic L-function. Over numberfields,it is mainly concerned with problems

on Shimura varieties: canonical models, the point of their reductions modulo prime

ideals, and Hasse-Weil zeta functions.

This Institute emphasized representations so that, at least formally, the primary

object of concern was an automorphic representation rather than an automorphic

form. However, there is no substantial difference between the two, and this should

not hide the fact that the theory is a direct outgrowth of the classical theory of

automorphic forms. In order to give a comprehensive treatment of our subject

matter and yet not produce too heavy a schedule, it was decided to omit a number

of topics on automorphic forms which do not fit well at present into the chosen

framework. For example, the Institute was planned to have little overlap with the

Conference on Modular Functions of One Variable held in Bonn (1976). The reader

is referred to the Proceedings of the latter (Springer Lecture Notes 601,627) and to

those of its predecessor (Springer Lecture Notes 320, 350, 476) for some of those

topics and a more classical point of view. Also, some topics of considerable interest

in themselves such as reductive groups, their infinite dimensional representations,

or moduli varieties, were discussed chiefly in function of the needs of the main

themes of the Institute.

These Proceedings appear in two parts, the first one contains sections I and II,

and the second one sections III and IV.

A. BOREL

W. CASSELMAN