Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields II |
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Authors: | Tomohiro Uchiyama |
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Institution: | 1. Division of Mathematics, National Center for Theoretical Sciences, National Taiwan University, Taipei, Taiwant.uchiyama2170@gmail.com |
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Abstract: | Let k be a separably closed field. Let G be a reductive algebraic k-group. 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 show that a regular reductive k-subgroup of G is G-completely reducible over k. We present examples where the number of overgroups of irreducible subgroups and the number of G(k)-conjugacy classes of k-anisotropic unipotent elements are infinite. |
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Keywords: | Algebraic groups complete reducibility pseudo-reductivity spherical buildings |
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