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The Balmer spectrum of rational equivariant cohomoloy theories
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Greenlees, John (2019) The Balmer spectrum of rational equivariant cohomoloy theories. Journal of Pure and Applied Algebra, 223 (7). pp. 2845-2871. doi:10.1016/j.jpaa.2018.10.001 ISSN 0022-4049.
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Official URL: https://doi.org/10.1016/j.jpaa.2018.10.001
Abstract
The category of rational G-equivariant cohomology theories for a compact Lie group G is the homotopy category of rational G-spectra and therefore tensor-triangulated. We show that its Balmer spectrum is the set of conjugacy classes of closed subgroups of G, with the topology corresponding to the topological poset of [7]. This is used to classify the collections of subgroups arising as the geometric isotropy of finite G-spectra. The ingredients for this classification are (i) the algebraic model of free spectra of the author and B. Shipley [14], (ii) the Localization Theorem of Borel–Hsiang–Quillen [21] and (iii) tom Dieck's calculation of the rational Burnside ring [4].
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Homology theory, Lie groups | ||||||||
| Journal or Publication Title: | Journal of Pure and Applied Algebra | ||||||||
| Publisher: | Elsevier Science BV | ||||||||
| ISSN: | 0022-4049 | ||||||||
| Official Date: | July 2019 | ||||||||
| Dates: |
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| Volume: | 223 | ||||||||
| Number: | 7 | ||||||||
| Page Range: | pp. 2845-2871 | ||||||||
| DOI: | 10.1016/j.jpaa.2018.10.001 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 22 February 2019 | ||||||||
| Date of first compliant Open Access: | 16 October 2019 | ||||||||
| Open Access Version: |
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