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Taylor towers for Γ -modules

Birgit Richter — 2001

Annales de l’institut Fourier

We consider Taylor approximation for functors from the small category of finite pointed sets Γ to modules and give an explicit description for the homology of the layers of the Taylor tower. These layers are shown to be fibrant objects in a suitable closed model category structure. Explicit calculations are presented in characteristic zero including an application to higher order Hochschild homology. A spectral sequence for the homology of the homotopy fibres of this approximation is provided.

Galois theory and Lubin-Tate cochains on classifying spaces

Andrew BakerBirgit Richter — 2011

Open Mathematics

We consider brave new cochain extensions F(BG +,R) → F(EG +,R), where R is either a Lubin-Tate spectrum E n or the related 2-periodic Morava K-theory K n, and G is a finite group. When R is an Eilenberg-Mac Lane spectrum, in some good cases such an extension is a G-Galois extension in the sense of John Rognes, but not always faithful. We prove that for E n and K n these extensions are always faithful in the K n local category. However, for a cyclic p-group C p r , the cochain extension F ( B C p r + , E n ) F ( E C p r + , E n ) is not a Galois...

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