Title: Galois extensions of structured ring spectra
Author: John Rognes
Author's e-mail address: rognes@math.uio.no
Abstract: 
We introduce the notion of a Galois extension of commutative S-algebras
(E-infinity ring spectra), often localized with respect to a fixed
homology theory.  There are numerous examples, including some involving
Eilenberg-Mac Lane spectra of commutative rings, real and complex
topological K-theory, Lubin-Tate spectra and cochain S-algebras.
We establish the main theorem of Galois theory in this generality.
Its proof involves the notions of separable (and etale) extensions
of commutative S-algebras, and the Goerss-Hopkins-Miller theory for
E-infinity mapping spaces.  We show that the global sphere spectrum~S
is separably closed (using Minkowski's discriminant theorem), and we
estimate the separable closure of its localization with respect to each
of the Morava K-theories.  We also define Hopf-Galois extensions of
commutative S-algebras, and study the complex cobordism spectrum MU as
a common integral model for all of the local Lubin-Tate Galois extensions.