John Rognes

"Galois theory of commutative S-algebras"

Abstract: The classical Galois theory of fields was extended to commutative rings by Auslander, Chase, Goldman, Harrison and Rosenberg around 1960. It now admits a further extension of interest to homotopy theorists, namely to the commutative S-algebras or E-infty ring spectra of Elmendorf, Kriz, Mandell and May. For example, the complexification map KO --> KU from real to complex K-theory is a Galois extension of commutative S-algebras with Galois group of order two. The talk will suggest why such extensions can be of arithmetic and geometric interest, and will present some of the fundamental theory of such Galois extensions.