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 |
| 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: | 08 Feb 2013 16:57 |
| 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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