BibTeX
@MISC{Gepner05homotopytopoi,
author = {David Gepner},
title = {HOMOTOPY TOPOI AND EQUIVARIANT ELLIPTIC COHOMOLOGY },
year = {2005}
}
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Abstract
We use the language of homotopy topoi, as developed by Lurie [17], Rezk [21], Simpson [23], and Töen-Vezossi [24], in order to provide a common foundation for equivariant homotopy theory and derived algebraic geometry. In particular, we obtain the categories of G-spaces, for a topological group G, and E-schemes, for an E∞-ring spectrum E, as full topological subcategories of the homotopy topoi associated to sheaves of spaces on certain small topological sites. This allows for a particularly elegant construction of the equivariant elliptic cohomology associated to an oriented elliptic curve A and a compact abelian Lie group G as an essential geometric morphism of homotopy topoi. It follows that our definition satisfies a conceptually simpler homotopy-theoretic analogue of the Ginzburg-Kapranov-Vasserot axioms [8], which allows us to calculate the cohomology of the equivariant G-spectra S V associated to representations V of G. iii To my parents.
Keyphrases
homotopy topos equivariant elliptic cohomology homotopy topos simpler homotopy-theoretic analogue common foundation elliptic curve compact abelian lie group certain small topological site algebraic geometry equivariant g-spectra topological group equivariant homotopy theory equivariant elliptic cohomology full topological subcategories ring spectrum elegant construction essential geometric morphism ginzburg-kapranov-vasserot axiom
