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 under a mild additional assumption.

Keywords

• 11G18
• 11F33
• 11F80
• Hecke algebras
• Galois representations
• Shimura varieties