Galois theory and Lubin-Tate cochains on classifying spaces

Baker, A. and Richter, B. (2011) Galois theory and Lubin-Tate cochains on classifying spaces. Central European Journal of Mathematics, 9(5), pp. 1074-1087. (doi: 10.2478/s11533-011-0058-3)

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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(BC p r +,E n ) → F(EC p r +, E n ) is not a Galois extension because it ramifies. As a consequence, it follows that the E n -theory Eilenberg-Moore spectral sequence for G and BG does not always converge to its expected target.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Baker, Dr Andrew
Authors: Baker, A., and Richter, B.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Research Group:Geometry & Topology
Journal Name:Central European Journal of Mathematics
ISSN (Online):1644-3616
Published Online:01 June 2011
Copyright Holders:Copyright © 2011 Versita
First Published:First published in Central European Journal of Mathematics 9(5):1074-1087
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.

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