| Abstract: | We determine the Galois representations inside the l-adic cohomology of certain Shimura varieties with bad reductions by the method of Langlands-Kottwitz. Here, some new phenomenons will appear when the local reductive groups are not quasi-split. For example, the usual Kottwtiz triples are not enough to parameterize the points on these Shimura varieties over finite fileds, and among others, one has to prove a vanishing result for the test functions to get the correct counting points formula. |
