# Galois theory and Lubin-Tate cochains on classifying spaces

Open Mathematics (2011)

- Volume: 9, Issue: 5, page 1074-1087
- ISSN: 2391-5455

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topAndrew Baker, and Birgit Richter. "Galois theory and Lubin-Tate cochains on classifying spaces." Open Mathematics 9.5 (2011): 1074-1087. <http://eudml.org/doc/269295>.

@article{AndrewBaker2011,

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 $F(BC_\{p^r + \} ,E_n ) \rightarrow F(EC_\{p^r + \} ,E_n )$ 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 BGdoes not always converge to its expected target.},

author = {Andrew Baker, Birgit Richter},

journal = {Open Mathematics},

keywords = {Lubin-Tate spectrum; Morava K-theory; Classifying spaces of finite groups; Galois extensions; Morava -theory; classifying spaces of finite groups},

language = {eng},

number = {5},

pages = {1074-1087},

title = {Galois theory and Lubin-Tate cochains on classifying spaces},

url = {http://eudml.org/doc/269295},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Andrew Baker

AU - Birgit Richter

TI - Galois theory and Lubin-Tate cochains on classifying spaces

JO - Open Mathematics

PY - 2011

VL - 9

IS - 5

SP - 1074

EP - 1087

AB - 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 $F(BC_{p^r + } ,E_n ) \rightarrow F(EC_{p^r + } ,E_n )$ 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 BGdoes not always converge to its expected target.

LA - eng

KW - Lubin-Tate spectrum; Morava K-theory; Classifying spaces of finite groups; Galois extensions; Morava -theory; classifying spaces of finite groups

UR - http://eudml.org/doc/269295

ER -

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