GL2, which constructs systems of /-adic representations whose L-series is a given
automorphic L-function. Over number fields, 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.