Abstract of talk by A. Baker (Glasgow)

Galois extensions of the K(n)-local sphere

The notion of a Galois extension of commutative S-algebras (= E-infinty
ring spectra) was introduced by John Rognes. While algebraic Galois theory
embeds into stable homotopy theory via Eilenberg-MacLane spectra, there
are many more subtle examples than those coming from algebra. For example,
KO --> KU gives an example of a Galois extension with group C_2. Rognes
showed that the sphere spectrum admits no connected Galois extensions with
finite Galois group, essentially because there are no unramified Galois
extensions of the rationals. On the other hand, the K(n)-local sphere
S_{K(n)} spectrum admits the Lubin-Tate spectra as Galois extensions with
profinite Galois group. I will discuss this and a recent result with
Birgit Richter which determines the 'algebraic closure' of S_{K(n)}.