Compactly supported cohomology and nearby cycle cohomology of open Shimura varieties of PEL type

Abstract

In this paper, we compare two cohomology groups associated to Shimura varieties of PEL type, which are not proper over the base. One is the compactly supported l-adic cohomology, and the other is the nearby cycle cohomology, namely, the compactly supported cohomology of the nearby cycle complex for the canonical integral model of the Shimura variety over Z_p. We prove that the G(Q_p)-cuspidal part of these cohomology groups are the same, where G denotes the reductive algebraic group naturally attached to the PEL datum. Some applications to unitary Shimura varieties are also given.

35 pages, typo corrected

References in corpus (2)

• Théorie de Lubin-Tate non abélienne l-entière
• Cuspidal representations in the l-adic cohomology of the Rapoport-Zink space for GSp(4)

Cited by in corpus (1)

• On the Hodge-Newton filtration for p-divisible groups with additional structures