Supercuspidal part of the mod l cohomology of GU(1,n - 1)-Shimura varieties
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...
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| Format: | Article |
| Language: | en_US |
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Walter de Gruyter
2017
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| Online Access: | http://hdl.handle.net/1721.1/108760 |
| _version_ | 1811090443628183552 |
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| author | Shin, Sug Woo |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Shin, Sug Woo |
| author_sort | Shin, Sug Woo |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T14:46:15Z |
| format | Article |
| id | mit-1721.1/108760 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:46:15Z |
| publishDate | 2017 |
| publisher | Walter de Gruyter |
| record_format | dspace |
| spelling | mit-1721.1/1087602022-09-29T10:26:14Z Supercuspidal part of the mod l cohomology of GU(1,n - 1)-Shimura varieties Shin, Sug Woo Massachusetts Institute of Technology. Department of Mathematics Shin, Sug Woo 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. 2017-05-08T20:34:48Z 2017-05-08T20:34:48Z 2017-07 2013-01 Article http://purl.org/eprint/type/JournalArticle 0075-4102 1435-5345 http://hdl.handle.net/1721.1/108760 Shin, Sug Woo. “Supercuspidal Part of the Mod L Cohomology of GU(1,n - 1)-Shimura Varieties.” Journal für die reine und angewandte Mathematik (Crelles Journal) 2015.705 (2015): 1–21. © 2015 De Gruyter en_US http://dx.doi.org/10.1515/crelle-2013-0057 Journal für die reine und angewandte Mathematik (Crelles Journal) Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Walter de Gruyter De Gruyter |
| spellingShingle | Shin, Sug Woo Supercuspidal part of the mod l cohomology of GU(1,n - 1)-Shimura varieties |
| title | Supercuspidal part of the mod l cohomology of GU(1,n - 1)-Shimura varieties |
| title_full | Supercuspidal part of the mod l cohomology of GU(1,n - 1)-Shimura varieties |
| title_fullStr | Supercuspidal part of the mod l cohomology of GU(1,n - 1)-Shimura varieties |
| title_full_unstemmed | Supercuspidal part of the mod l cohomology of GU(1,n - 1)-Shimura varieties |
| title_short | Supercuspidal part of the mod l cohomology of GU(1,n - 1)-Shimura varieties |
| title_sort | supercuspidal part of the mod l cohomology of gu 1 n 1 shimura varieties |
| url | http://hdl.handle.net/1721.1/108760 |
| work_keys_str_mv | AT shinsugwoo supercuspidalpartofthemodlcohomologyofgu1n1shimuravarieties |