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 , the cochain extension 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 BGdoes not always converge to its expected target.
@article{bwmeta1.element.doi-10_2478_s11533-011-0058-3,
author = {Andrew Baker and Birgit Richter},
title = {Galois theory and Lubin-Tate cochains on classifying spaces},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {1074-1087},
zbl = {1236.55014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0058-3}
}
Andrew Baker; Birgit Richter. Galois theory and Lubin-Tate cochains on classifying spaces. Open Mathematics, Tome 9 (2011) pp. 1074-1087. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0058-3/
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