On the \(\lambda\)-adic representations associated to some simple Shimura varieties (Q1204250)

This paper is a contribution to the programme of associating \(\lambda\)- adic Galois representations to ``cohomological'' automorphic representations. The author points out that when one has a \(CM\) field \(F\) and a division algebra \(D\) defined and central over \(F\) then the Shimura varieties which are `moduli spaces for abelian varieties with complex multiplication by \(D\)' are particularly susceptible to analysis. He proves a very sharp theorem of the type mentioned above but it would take too much preparation to repeat the formulation here. The proof uses a ``pseudo-stabilized'' trace formula and a comparison with the Lefschetz formula. It is the consequence of a series of papers published by the author and this paper relies heavily on its predecessors.