Galois extensions of Lubin-Tate spectra

Abstract

Let En be the n-th Lubin-Tate spectrum at a prime p. There is a commutative S-algebra E nr n whose coecients are built from the coecients of En 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 with Galois group a finite group G with cyclic quotient. Our results carry over to the K(n)-local context.