On the l-adic cohomology of some p-adically uniformized Shimura varieties

2014/11/02 by Xu Shen, Shen, Xu
Mathematics · #11G18 #14G35 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G18 #msc:14G35

paper · pdf · doi:10.48550/arxiv.1411.0244

25 pages, slightly revised version, to appear in Journal of the Institute of Mathematics of Jussieu

arxiv created 2016/11/13 · arxiv updated 2016/11/15

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.

Related

• p-adic uniformization of unitary Shimura varieties II
• p-adic uniformization of unitary Shimura varieties
• l-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients
• New cases of p-adic uniformization
• Towards a theory of local Shimura varieties