Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups

Erscheinungsjahr 2008
ISBN: 978-0-8218-4076-4
Verlag: American Mathematical Society

Buch, Englisch, 137 Seiten, Format (B × H): 204 mm x 255 mm, Gewicht: 236 g

Reihe: Memoirs of the American Mathematical Society

The author introduces the notion of a Galois extension of commutative $S$-algebras ($E \infty$ 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. He establishes 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 $E \infty$ mapping spaces. He shows that the global sphere spectrum $S$ is separably closed, using Minkowski's discriminant theorem, and he estimates the separable closure of its localization with respect to each of the Morava $K$-theories. He also defines Hopf-Galois extensions of commutative $S$-algebras and studies the complex cobordism spectrum $MU$ as a common integral model for all of the local Lubin-Tate Galois extensions.

Autoren/Hrsg.

Rognes, John

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie