Homology, Homotopy and Applications

Galois extensions of Lubin-Tate spectra

Andrew Baker and Birgit Richter

Full-text: Open access

Abstract

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 a.re 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 a.re 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.

Article information

Source
Homology Homotopy Appl., Volume 10, Number 3 (2008), 27-43.

Dates
First available in Project Euclid: 1 September 2009

Permanent link to this document
https://projecteuclid.org/euclid.hha/1251832466

Mathematical Reviews number (MathSciNet)
MR2475616

Zentralblatt MATH identifier
1175.55007

Subjects
Primary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) 13B05: Galois theory 13K05 55P60: Localization and completion 55N22: Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]

Keywords
Galois extensions separable closure Witt vectors Lubin-Tate spectra

Citation

Baker, Andrew; Richter, Birgit. Galois extensions of Lubin-Tate spectra. Homology Homotopy Appl. 10 (2008), no. 3, 27--43. https://projecteuclid.org/euclid.hha/1251832466


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