ON THE L-adic COHOMOLOGY OF SOME p-ADICALLY UNIFORMIZED SHIMURA VARIETIES

Abstract

We determine the Galois representations inside the l-adic cohomology of some unitary Shimura varieties at split places where they admit uniformization by finite products of Drinfeld upper half spaces. Our main results confirm Langlands-Kottwitz's description of the cohomology of Shimura varieties in new cases.