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An algebraic model for rational naïve-commutative ring SO(2)-spectra and equivariant elliptic cohomology
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Barnes, David, Greenlees, John and Kędziorek, Magdalena (2021) An algebraic model for rational naïve-commutative ring SO(2)-spectra and equivariant elliptic cohomology. Mathematische Zeitschrift, 297 . pp. 1205-1235. doi:10.1007/s00209-020-02554-0 ISSN 0025-5874.
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Official URL: https://doi.org/10.1007/s00209-020-02554-0
Abstract
Equipping a non-equivariant topological E∞-operad with the trivial G-action gives an operad in G-spaces. For a G-spectrum, being an algebra over this operad does not provide any multiplicative norm maps on homotopy groups. Algebras over this operad are called naïve-commutative ring G-spectra. In this paper we take G=SO(2) and we show that commutative algebras in the algebraic model for rational SO(2)-spectra model rational naïve-commutative ring SO(2)-spectra. In particular, this applies to show that the SO(2)-equivariant cohomology associated to an elliptic curve C of Greenlees (Topology 44(6):1213–1279, 2005) is represented by an E∞-ring spectrum. Moreover, the category of modules over that E∞-ring spectrum is equivalent to the derived category of sheaves over the elliptic curve C with the Zariski torsion point topology.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Algebra, Homological | |||||||||
| Journal or Publication Title: | Mathematische Zeitschrift | |||||||||
| Publisher: | Springer | |||||||||
| ISSN: | 0025-5874 | |||||||||
| Official Date: | April 2021 | |||||||||
| Dates: |
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| Volume: | 297 | |||||||||
| Page Range: | pp. 1205-1235 | |||||||||
| DOI: | 10.1007/s00209-020-02554-0 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Copyright Holders: | © The Author(s) 2020 | |||||||||
| Date of first compliant deposit: | 3 September 2020 | |||||||||
| Date of first compliant Open Access: | 4 September 2020 | |||||||||
| RIOXX Funder/Project Grant: |
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