Supercuspidal part of the mod <i>l</i> cohomology of GU(1,<i>n</i> - 1)-Shimura varieties

Abstract

Abstract Let l be a prime. In this paper we are concerned with GU(1, n - 1)-type Shimura varieties with arbitrary level structure at l and investigate the part of the cohomology on which G (ℚ p ) acts through mod l supercuspidal representations, where p ≠ l is any prime such that G (ℚ p ) is a general linear group. The main theorem establishes the mod l analogue of the local-global compatibility. Our theorem also encodes a global mod l Jacquet–Langlands correspondence in that the cohomology is described in terms of mod l automorphic forms on some compact inner form of G .

Locations

• DSpace@MIT (Massachusetts Institute of Technology) - View - PDF
• Journal für die reine und angewandte Mathematik (Crelles Journal) - View