 
Summary: Fields Institute Communications
Volume 60, 2011
lArlie Etale Cohomology of PEL Type Shimura Varieties
with N onTrivial Coefficients
Elena Mantovan
Mathematics 25337
Caltech
Pasadena, CA 91125 USA
mantovan~caltech.edu
Abstract. Given a Shimura datum (C, h) of PEL type, let p be an
odd prime at which G is unramified. In [13], we established a formula
computing the ladic cohomology of the associated Shimura varieties
(regarded as a representation of the adelic points of G and of the local
Weil group at p) in terms of that oftheir local models at p (the associated
RapoportZink spaces) and of the corresponding Igusa varieties. In this
paper we extend those results (which are for cohomology with constant
ladic coefficients) to the general case of coefficients in a lisse etale sheaf
attached to a finite dimensionalladic representation of the group C.
1 Introduction
To any reductive group G defined over a number field, one can associate a
