Floer cohomology of ind-schemes
-- Mikhail Kapranov, February 27, 2004

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The talk is based on work in progress with S. Arkhipov. 
We develop a theory of semiinfinite (Floer) cohomology of
an appropriate class of algebro-geometric objects (ind-schemes
of locally compact type). Our approach is based on algebraic
geometry, not Morse theory. The examples include:
the "projective space" associated to a Tate vector space
such as C((t)) (Laurent series with complex coefficients) and
various models for loop spaces in the spirit of Givental and
Vlassopoulos.