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Title:Homotopy Topoi and Equivariant Elliptic Cohomology
Author(s):Gepner, David J.
Doctoral Committee Chair(s):Ando, Matthew
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
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.
Issue Date:2006
Description:67 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006.
Other Identifier(s):(MiAaPQ)AAI3223594
Date Available in IDEALS:2015-09-28
Date Deposited:2006

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