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Some properties of Lubin-Tate cohomology for classifying spaces of finite groups

2010/05/10 by Andrew Baker, Baker, Andrew, Birgit Richter +1
Mathematics · #13B05 (Secondary) #55N22 #55P43 (Primary) #55P60 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.AT #math.RA #msc:13B05 #msc:55N22 #msc:55P43 #msc:55P60

paper · pdf · doi:10.48550/arxiv.1005.1662

Minor changes, section on Frobenius algebra structure removed. Final version: to appear in Central European Journal of Mathematics under title `Galois theory and Lubin-Tate cochains on classifying spaces'

openalex publication_date 2010/05/10 · arxiv created 2011/05/31 · arxiv updated 2011/06/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider brave new cochain extensions F(BG+,R)→ F(EG+,R), where R is either a Lubin-Tate spectrum En or the related 2-periodic Morava K-theory Kn, 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 En and Kn these extensions are always faithful in the Kn local category. However, for a cyclic p-group Cpr, the cochain extension F(BCpr+,En) → F(ECpr+,En) is not a Galois extensions because it ramifies. As a consequence, it follows that the En-theory Eilenberg-Moore spectral sequence for G and BG does not always converge to its expected target.

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