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Rational S^1-equivariant elliptic cohomology

Greenlees, J.P.C. (2005) Rational S^1-equivariant elliptic cohomology. Topology, 44 (6). pp. 1213-1279. ISSN 0040-9383

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Abstract

For each elliptic curve A over the rational numbers we construct a 2-periodic S^1-equivariant cohomology theory E whose cohomology ring is the sheaf cohomology of A; the homology of the sphere of the representation z^n is the cohomology of the divisor A(n) of points with order dividing n. The construction proceeds by using the algebraic models of the author's AMS Memoir ``Rational S^1 equivariant homotopy theory.'' and is natural and explicit in terms of sheaves of functions on A. This is Version 5.2 of a paper of long genesis (this should be the final version). The following additional topics were first added in the Fourth Edition: (a) periodicity and differentials treated (b) dependence on coordinate (c) relationship with Grojnowksi's construction and, most importantly, (d) equivalence between a derived category of O_A-modules and a derived category of EA-modules. The Fifth Edition included (e) the Hasse square and (f) explanation of how to calculate maps of EA-module spectra.

Item Type: Article
Copyright, Publisher and Additional Information: Imported from arXiv
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Beccy Shipman
Date Deposited: 04 Mar 2009 17:50
Last Modified: 18 Jun 2014 06:14
Published Version: http://dx.doi.org/10.1016/j.top.2005.05.002
Status: Published
Publisher: Elsevier
Identification Number: 10.1016/j.top.2005.05.002
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/7806

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