Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups (Memoirs of the American Mathematical Society, Band 192) - Softcover

Rognes, John

Softcover

ISBN 10: 0821840762 ISBN 13: 9780821840764

Verlag: American Mathematical Society, 2008

Inhaltsangabe

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.

Details zur Ausgabe

• Verlag: American Mathematical Society
• Erscheinungsdatum: 2008
• Sprache: Englisch
• ISBN 10: 0821840762
• ISBN 13: 9780821840764
• Einband: Taschenbuch
• Anzahl der Seiten: 137
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar