Summary: ~ ~ - c o h o m o l o ~ ~and automorphic representations
The University of Toronto
Abstract. This article is an introduction to the L~-cohomologyof arithmetic symmetric
spaces. We shall describe properties of automorphic representations which lead to a
remarkable interplay amongHodge structures,Lefschetzstructures,and Hecke operators.
In order to make the discussion slightly more concrete, we shall focus on the special case
of Siegel moduli space.
Resume. Cet article est une introduction a la cohomologie L2 des espaces
symetriques arithmetiques. On dkcrit des propriktks des representations automorphes
ou interagissent de facon remarquahle les structures de Hodge et de Lefschetz et les
opkrateurs de Hecke. Pour fixer les idkes, on se restreint au cas particulier des espaces
de modules de Siegel.
I was asked by the editors to submit a general article on the trace
formula. There are severalsuchpapers already ,,[61,[231,[IS],and
I was not sure I could add anything. I decided to write a survey article on
a different topic, oneto which the trace formulahas been applied and will
certainly be applied further.
The article is on the relationship between L2-cohomologyand auto-
morphic representations. It is an introduction of sorts to the papers