Vanishing theorems for the mod $p$ cohomology of some simple Shimura varieties

Abstract

We show that the mod $p$ cohomology of a simple Shimura variety treated in Harris-Taylor's book vanishes outside a certain nontrivial range after localizing at any non-Eisenstein ideal of the Hecke algebra. In cases of low dimensions, we show the vanishing outside the middle degree.

arXiv comment11 pages, to appear in Forum Math. Sigma

References in corpus (1)

• p-adic Hodge-theoretic properties of étale cohomology with mod p coefficients, and the cohomology of Shimura varieties