Title of Paper: The homotopy fixed point spectra of profinite Galois extensions
Authors: Mark Behrens, Daniel G. Davis

AMS Classification numbers: 55N20, 55P43
ArXiv ID: math.AT/0808.1092
Email address of authors: mbehrens@math.mit.edu, dgdavis@louisiana.edu

Abstract: Let E be a k-local profinite G-Galois extension of
an E_\infty-ring spectrum A (in the sense of Rognes). We 
show that E may be regarded as producing a discrete G-spectrum.
Also, we prove that if E is a profaithful k-local profinite 
extension which satisfies certain extra conditions, then the 
forward direction of Rognes's Galois correspondence extends 
to the profinite setting. We show the function spectrum 
F_A((E^hH)_k, (E^hK)_k) is equivalent to the homotopy fixed 
point spectrum ((E[[G/H]])^hK)_k where H and K are closed 
subgroups of G. Applications to Morava E-theory are given, 
including showing that the homotopy fixed points defined by 
Devinatz and Hopkins for closed subgroups of the extended 
Morava stabilizer group agree with those defined with respect 
to a continuous action and in terms of the derived functor 
of fixed points.