Homotopy Topoi and Equivariant Elliptic Cohomology

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Gepner, David J.

Contributors dc:contributor

• Ando, Matthew

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3223594

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86859