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Higher de Rham cohomology

Lars Hesselholt
(Københavns Universitet)
Topology Seminar
Tuesday, 6 June, 2017, at 14:15, in Aud. D3 (1531-215)
Abstract:
Topological Hochschild homology introduced by Bökstedt in the
late eighties is a manifestation of the dual visions of Connes and Waldhausen
to extend de Rham cohomology to the noncommutative setting and to
replace algebra by higher algebra. In this expanded setting, topological
Hochschild homology takes the place of differential forms; the de Rham
differential is replaced by an action of the circle group; and de Rham
cohomology is replaced by the Tate cohomology of said circle action. The
resulting cohomology theory has had numerous applications to algebraic K-
theory and, more recently, to integral p-adic Hodge theory. This lecture
will give an introduction to recent developments in this theory and discuss
future goals.
Contact person: Marecl Bökstedt