Rational S 1 - Equivariant Elliptic Cohomology
نویسندگان
چکیده
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 [6]. Contents 1. Introduction. 1 2. Formal groups from complex oriented theories. 3 3. The model for rational T-spectra. 5 4. The affine case: T-equivariant cohomology theories from additive and multiplicative groups. 9 5. Elliptic curves. 13 6. Coordinate data 14 7. Local cohomology sheaves on elliptic curves. 15 8. A cohomology theory associated to an elliptic curve. 17 9. Multiplicative properties. 20 References 21
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