Geodesic
Galois extensions of Lubin-Tate spectra
Homology, homotopy, and applications, Tome 10 (2008) no. 3, pp. 27-43.

Voir la notice de l'article provenant de la source International Press of Boston

Let $E_n$ be the $n$-th Lubin-Tate spectrum at a prime $p$. There is a commutative $S$-algebra $E^{\mathrm{nr}}_n$ whose coefficients are 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 $E^{\mathrm{nr}}_n$ 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 are no non-trivial connected Galois extensions of $E^{\mathrm{nr}}_n$ with Galois group a finite group $G$ with cyclic quotient. Our results carry over to the $K(n)$-local context.
DOI : 10.4310/HHA.2008.v10.n3.a3
Classification : 13B05, 55N22, 55P43, 55P60
Keywords: Galois extensions, separable closure, Witt vectors, Lubin-Tate spectra 
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     author = {Andrew Baker and Birgit Richter},
     title = {Galois extensions of {Lubin-Tate} spectra},
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     pages = {27--43},
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Andrew Baker; Birgit Richter. Galois extensions of Lubin-Tate spectra. Homology, homotopy, and applications, Tome 10 (2008) no. 3, pp. 27-43. doi : 10.4310/HHA.2008.v10.n3.a3. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n3.a3/

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