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Fields Institute Communications Volume 60, 2011

Summary: Fields Institute Communications
Volume 60, 2011
l-Arlie Etale Cohomology of PEL Type Shimura Varieties
with N on-Trivial Coefficients
Elena Mantovan
Mathematics 253-37
Pasadena, CA 91125 USA
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 l-adic 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
Rapoport-Zink spaces) and of the corresponding Igusa varieties. In this
paper we extend those results (which are for cohomology with constant
l-adic coefficients) to the general case of coefficients in a lisse etale sheaf
attached to a finite dimensionall-adic representation of the group C.
1 Introduction
To any reductive group G defined over a number field, one can associate a


Source: Adolphs, Ralph - Psychology and Neuroscience, California Institute of Technology


Collections: Biology and Medicine