The homotopy fixed point theorem in algebraic Ktheory
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 Marco Schlichting (Warwick)
 Wednesday 02 November 2011, 14:1515:15
 MR13, CMS.
If you have a question about this talk, please contact Burt Totaro.
It is a classical theorem that the topological real vector bundle
Ktheory
KO(X) of a space X can be recovered from the simpler complex vector bundle K
theory KU(X). More precisely, KO(X) is equivalent to the space of homotopy
fixed points
of KU(X) under a natural involution.
In this talk I will explain to what extent the algebraic analogue holds
where real vector bundle Ktheory is replaced with higher GrothendieckWitt
groups (aka algebraic hermitian Ktheory) and complex vector bundle Ktheory
with ordinary algebraic Ktheory.
The proof of our main theorem uses a version of the QuillenLichtenbaum
conjecture for hermitian Ktheory which is of independent interest. This is
joint work with Berrick, Karoubi and Ostvaer.
This talk is part of the Algebraic Geometry Seminar series.
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