Greenlees, J.P.C. (2005) Rational S^1-equivariant elliptic cohomology. Topology, 44 (6). pp. 1213-1279. ISSN 0040-9383
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.
|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:||17 Nov 2015 17:11|