Homotopy Topoi and Equivariant Elliptic Cohomology
Gepner, David J.
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https://hdl.handle.net/2142/86859
Description
Title
Homotopy Topoi and Equivariant Elliptic Cohomology
Author(s)
Gepner, David J.
Issue Date
2006
Doctoral Committee Chair(s)
Ando, Matthew
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
We use the language of homotopy topoi, as developed by Lurie [17], Rezk [21], Simpson [23], and ToenVezossi [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 Einfinity-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.
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