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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2015, Issue 705


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

Sug Woo Shin
  • Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA; and Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722, Republic of Korea
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Published Online: 2013-07-17 | DOI: https://doi.org/10.1515/crelle-2013-0057


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 pl 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.

About the article

Received: 2011-11-04

Revised: 2013-01-13

Published Online: 2013-07-17

Published in Print: 2015-08-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2015, Issue 705, Pages 1–21, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2013-0057.

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