The homotopy fixed point theorem in algebraic K-theory

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• Marco Schlichting (Warwick)
• Wednesday 02 November 2011, 14:15-15:15
• 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 K-theory 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 K-theory is replaced with higher Grothendieck-Witt groups (aka algebraic hermitian K-theory) and complex vector bundle K-theory with ordinary algebraic K-theory. The proof of our main theorem uses a version of the Quillen-Lichtenbaum conjecture for hermitian K-theory 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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