Open Access
2008 Galois extensions of Lubin-Tate spectra
Andrew Baker, Birgit Richter
Homology Homotopy Appl. 10(3): 27-43 (2008).


Let $E_n$ be the $n$-th Lubin-Tate spectrum at a prime $p$ . There is a commutative $S$-algebra $E^{\rm{nr}}_n$ whose coefficients built from the coefficients of $E_n$ and contain all roots of unity whose order is not divisible by $p$. For odd primes $p$ we show that $E^{\rm{nr}}_n$ does not have any non-trivial connected finite Galois extensions and is thus separably closed in the sense of Rognes. At the prime 2 we prove that there no non-trivial connected Galois extensions of $E^{\rm{nr}}_n$ with Galois group a finite group $G$ with cyclic quotient. Our results carry over to the $K(n)$-local context.


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Andrew Baker. Birgit Richter. "Galois extensions of Lubin-Tate spectra." Homology Homotopy Appl. 10 (3) 27 - 43, 2008.


Published: 2008
First available in Project Euclid: 1 September 2009

zbMATH: 1175.55007
MathSciNet: MR2475616

Primary: 13B05 , 13K05 , 55N22 , 55P43 , 55P60

Keywords: Galois extensions , Lubin-Tate spectra , separable closure , Witt vectors

Rights: Copyright © 2008 International Press of Boston

Vol.10 • No. 3 • 2008
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