dc.contributor.author |
Uchiyama, Tomohiro |
en |
dc.date.accessioned |
2016-07-04T22:56:14Z |
en |
dc.date.issued |
2016-03 |
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dc.identifier.citation |
arXiv.org, 2016 |
en |
dc.identifier.uri |
http://hdl.handle.net/2292/29309 |
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dc.description.abstract |
Let k be a separably closed field. Let G be a reductive algebraic k-group. In this paper, we study Serre's notion of complete reducibility of subgroups of G over k. In particular, using the recently proved center conjecture of Tits, we show that the centralizer of a k-subgroup H of G is G-completely reducible over k if it is reductive and H is G-completely reducible over k. We also show that a regular reductive k-subgroup of G is G-completely reducible over k. Various open problems concerning complete reducibility are discussed. We present examples where the number of overgroups of irreducible subgroups and the number of G(k)-conjugacy classes of unipotent elements are infinite. This paper complements the author's previous work on rationality problems for complete reducibility. |
en |
dc.description.uri |
http://arxiv.org/abs/1512.04616v3 |
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dc.relation.ispartofseries |
arXiv.org |
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dc.rights |
Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from https://arxiv.org/ |
en |
dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
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dc.subject |
math.GR |
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dc.title |
Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields 2 |
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dc.type |
Journal Article |
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pubs.author-url |
http://arxiv.org/abs/1512.04616 |
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dc.rights.accessrights |
http://purl.org/eprint/accessRights/RestrictedAccess |
en |
pubs.subtype |
Article |
en |
pubs.elements-id |
514471 |
en |
pubs.arxiv-id |
1512.04616 |
en |
pubs.record-created-at-source-date |
2016-07-05 |
en |