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

• Main Author: Shin, Sug Woo (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: Walter de Gruyter, 2017-05-08T20:34:48Z.
• Subjects: Article
• Online Access: Get fulltext

 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[subscript p]) acts through mod l supercuspidal representations, where p ≠ l is any prime such that G(ℚ[subscript 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.