Title: Rognes's theory of Galois extensions and the continuous action 
       of G_n on E_n
Author: Daniel G. Davis
E-mail: dgdavis@math.purdue.edu
Address: Purdue University
Abstract: Let us take for granted that $L_{K(n)}S^0 \rightarrow E_n$ is 
some kind of a G_n-Galois extension. Of course, this is in the setting of 
continuous G_n-spectra. How much structure does this continuous G-Galois 
extension have? How much structure does one want to build into this 
notion to obtain useful conclusions? If the author's conjecture that 
"E_n/I, for a cofinal collection of I's, is a discrete G_n-symmetric ring 
spectrum" is true, what additional structure does this give the 
continuous G_n-Galois extension? Is it useful or merely beautiful? This 
paper is an exploration of how to answer these questions. This inactive 
manuscript arose as a letter to John Rognes, whom he thanks for a helpful 
conversation in Rosendal. This paper was written before John's preprints 
(the initial version and the final one) on Galois extensions were 
available. The author thanks Paul Goerss for his encouragement.