Title: Rational S^1-equivariant elliptic cohomology
Authors:J.P.C.Greenlees, M.J.Hopkins and I.Rosu
AMS Class numbers: 55N34, 55N91, 55P42, 55P62
\address{JPCG: Department of Pure Mathematics, Hicks Building,
Sheffield S3 7RH. UK.}
\email{j.greenlees@sheffield.ac.uk}
\address{MJH: Department of Mathematics, MIT, Cambridge, MA 02139-4307, USA.}
\email{mjh@math.mit.edu}
\address{IR: Department of Mathematics, MIT, Cambridge, MA 02139-4307, USA.}
\email{ioanid@math.mit.edu}
Abstract: We give a functorial construction of a rational
$S^1$-equivariant cohomology theory from an elliptic curve equipped
with suitable coordinate data. The
elliptic curve may be recovered from the cohomology theory; indeed,
the value of the cohomology theory on the compactification of an
$S^1$-representation is given by the sheaf cohomology of a suitable
line bundle on the curve. The construction is easy: by considering
functions on the elliptic curve with specified poles one may
write down the representing $S^1$-spectrum
in the first author's algebraic model of rational $S^1$-spectra.