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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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
• Publisher: Versita
• ISSN: 1895-1074
• 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.