Rognes's theory of Galois extensions and the continuous action of G_n on E_n

Details Rognes's theory of Galois extensions and the continuous action of G_n on E_n Rognes's theory of Galois extensions and the continuous action of G_n on E_n

2006-11-30

arxiv.org/abs/math/0611943v1

Mathematics

Algebraic Topology

date of last revision of preprint: 5/14/04; 14 pages

Scientific paper

Let us take for granted that L_{K(n)}S^0 --> 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 preprint 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.

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