Rational S^1-equivariant elliptic cohomology
Abstract
Description
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.
62 pages, no figures
62 pages, no figures