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Galois theory and Lubin-Tate cochains on classifying spaces

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Baker A., Richter B.

Open Mathematics

2011

tom 9

nr 5

1074-1087

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 $F(BC_{p^r + } ,E_n ) \to F(EC_{p^r + } ,E_n )$ 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.

Ograniczanie wyników

1 Open Mathematics

1 Baker A.

1 Richter B.

1 2011

Wyniki wyszukiwania

Galois theory and Lubin-Tate cochains on classifying spaces