Supercuspidal part of the mod l cohomology of GU(1,n - 1)-Shimura varieties
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Sug Woo Shin
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(ℚp) acts through mod l supercuspidal representations, where p ≠ l is any prime such that G(ℚp) 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.
The reader will clearly see the great influence of Jean-Francois Dat's work on this paper. I am grateful to Dat for his kind answers to numerous questions and Kai-Wen Lan for encouraging me on this problem. I appreciate Naoki Imai and Yoichi Mieda for sending me their recent preprint [`Compactly supported cohomology of nearby cycle cohomology of open Shimura varietes of PEL type', preprint 2011]. I heartily thank the referee for a careful reading, pointing out several inaccuracies, and suggestions to improve the paper.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Supercuspidal part of the mod l cohomology of GU(1,n - 1)-Shimura varieties
- Algebraic and rigid geometry on the Schottky problem
- Topological full groups of one-sided shifts of finite type
- Ricci curvature and Lp-convergence
- Weak multiplier Hopf algebras I. The main theory
- Families of abelian varieties with many isogenous fibres
- Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below
Articles in the same Issue
- Frontmatter
- Supercuspidal part of the mod l cohomology of GU(1,n - 1)-Shimura varieties
- Algebraic and rigid geometry on the Schottky problem
- Topological full groups of one-sided shifts of finite type
- Ricci curvature and Lp-convergence
- Weak multiplier Hopf algebras I. The main theory
- Families of abelian varieties with many isogenous fibres
- Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below
