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Rational $\mathrm{SO}(2)$–equivariant spectra

David Barnes, J P C Greenlees, Magdalena Kędziorek and Brooke Shipley

Algebraic & Geometric Topology 17 (2017) 983–1020
Abstract

We prove that the category of rational SO(2)–equivariant spectra has a simple algebraic model. Furthermore, all of our model categories and Quillen equivalences are monoidal, so we can use this classification to understand ring spectra and module spectra via the algebraic model.

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Keywords
equivariant spectra, model categories, right Bousfield localization, algebraic models, ring spectra
Mathematical Subject Classification 2010
Primary: 55N91, 55P42, 55P60
References
Publication
Received: 13 November 2015
Revised: 14 July 2016
Accepted: 19 October 2016
Published: 14 March 2017
Authors
David Barnes
Pure Mathematics Research Centre
Queen’s University Belfast
University Road
Belfast
BT7 1NN
United Kingdom
http://www.qub.ac.uk/puremaths/Staff/David\%20Barnes/index.html
J P C Greenlees
School of Mathematics and Statistics
University of Sheffield
The Hicks Building
Sheffield
S3 7RH
United Kingdom
http://www.greenlees.staff.shef.ac.uk/
Magdalena Kędziorek
MATHGEOM
École Polytechnique Fédérale de Lausanne
CH-1015 Lausanne
Switzerland
http://people.epfl.ch/magdalena.kedziorek
Brooke Shipley
Department of Mathematics, Statistics and Computer Science
University of Illinois at Chicago
508 SEO m/c 249
851 S. Morgan Street
Chicago, IL 60607-7045
United States
http://homepages.math.uic.edu/~bshipley/