Unipotent elements in small characteristic
Let G be a reductive connected algebraic group over an algebraically closed field of characteristic exponent p ≥ 1. One of the aims of this paper is to present a picture of the unipotent elements of G which should apply for arbitrary p and is as close as possible to the picture for p = 1. Another ai...
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| Format: | Article |
| Language: | English |
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Springer Nature America, Inc
2022
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| Online Access: | https://hdl.handle.net/1721.1/140246 |
| _version_ | 1811081540592992256 |
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| author | Lusztig, G |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Lusztig, G |
| author_sort | Lusztig, G |
| collection | MIT |
| description | Let G be a reductive connected algebraic group over an algebraically closed field of characteristic exponent p ≥ 1. One of the aims of this paper is to present a picture of the unipotent elements of G which should apply for arbitrary p and is as close as possible to the picture for p = 1. Another aim is the study of Bu, the variety of Borel subgroups of G containing a unipotent element u. It is known [Sp] that when p is a good prime, the l-adic cohomology spaces of Bu are pure. We would like to prove a similar result in the case where p is a bad prime. We present a method by which this can be achieved in a number of cases. |
| first_indexed | 2024-09-23T11:48:10Z |
| format | Article |
| id | mit-1721.1/140246 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:48:10Z |
| publishDate | 2022 |
| publisher | Springer Nature America, Inc |
| record_format | dspace |
| spelling | mit-1721.1/1402462024-06-06T14:42:38Z Unipotent elements in small characteristic Lusztig, G Massachusetts Institute of Technology. Department of Mathematics Let G be a reductive connected algebraic group over an algebraically closed field of characteristic exponent p ≥ 1. One of the aims of this paper is to present a picture of the unipotent elements of G which should apply for arbitrary p and is as close as possible to the picture for p = 1. Another aim is the study of Bu, the variety of Borel subgroups of G containing a unipotent element u. It is known [Sp] that when p is a good prime, the l-adic cohomology spaces of Bu are pure. We would like to prove a similar result in the case where p is a bad prime. We present a method by which this can be achieved in a number of cases. 2022-02-09T18:51:41Z 2022-02-09T18:51:41Z 2005-12 2022-02-09T18:41:26Z Article http://purl.org/eprint/type/JournalArticle 1531-586X 1083-4362 https://hdl.handle.net/1721.1/140246 Lusztig, G. Unipotent elements in small characteristic. Transformation Groups 10, 449–487 (2005) en 10.1007/s00031-005-0405-1 Transformation Groups 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 Springer Nature America, Inc arXiv |
| spellingShingle | Lusztig, G Unipotent elements in small characteristic |
| title | Unipotent elements in small characteristic |
| title_full | Unipotent elements in small characteristic |
| title_fullStr | Unipotent elements in small characteristic |
| title_full_unstemmed | Unipotent elements in small characteristic |
| title_short | Unipotent elements in small characteristic |
| title_sort | unipotent elements in small characteristic |
| url | https://hdl.handle.net/1721.1/140246 |
| work_keys_str_mv | AT lusztigg unipotentelementsinsmallcharacteristic |