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Ando, Matthew Gepner, David J. 2015-09-28T15:19:53Z 2015-09-28T15:19:53Z 10000-01-01 2006 2006 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. Made available in DSpace on 2015-09-28T15:19:53Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3223594.pdf: 1756076 bytes, checksum: a3cf23e510b9b629f8476883bd915458 (MD5) Previous issue date: 2006 Embargo set by: Seth Robbins for item 88140 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 67 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. http://hdl.handle.net/2142/86859 (MiAaPQ)AAI3223594 eng Mathematics Homotopy Topoi and Equivariant Elliptic Cohomology text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.