Galois extensions of Lubin-Tate spectra

Details Galois extensions of Lubin-Tate spectra Galois extensions of Lubin-Tate spectra

2007-10-26

arxiv.org/abs/0710.5097v4

Mathematics

Algebraic Topology

revised version in final form

Scientific paper

Let E_n be the n-th Lubin-Tate spectrum at a prime p. There is a commutative S-algebra E^{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^{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^{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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