Rational S^1-equivariant elliptic cohomology
| Autor: | J. P. C. Greenlees |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2005 |
| Předmět: |
Pure mathematics
Group cohomology Equivariant cohomology Rational S1-spectra Elliptic cohomology Mathematics::Algebraic Topology Cohomology Cohomology ring Motivic cohomology Algebra Mathematics::Algebraic Geometry Mathematics::K-Theory and Homology Mathematics::Category Theory De Rham cohomology FOS: Mathematics 55N34 55N91 (Primary) 14H52 (Secondary) Elliptic curves Algebraic Topology (math.AT) Geometry and Topology Mathematics - Algebraic Topology Čech cohomology Mathematics |
| ISSN: | 0040-9383 |
| Popis: | 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 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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