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Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups

Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups

Buch | Softcover
137 Seiten
2008
American Mathematical Society (Verlag)
978-0-8218-4076-4 (ISBN)
CHF 118,70 inkl. MwSt
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Introduces the notion of a Galois extension of commutative $S$-algebras ($E_/infty$ ring spectra), often localized with respect to a fixed homology theory. The author establishes the main theorem of Galois theory.
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.

Galois Extensions of Structured Ring Spectra: Abstract Introduction Galois extensions in algebra Closed categories of structured module spectra Galois extensions in topology Examples of Galois extensions Dualizability and alternate characterizations Galois theory I Pro-Galois extensions and the Amitsur complex Separable and etale extensions Mapping spaces of commutative $S$-algebras Galois theory II Hopf-Galois extensions in topology References Stably Dualizable Groups: Abstract Introduction The dualizing spectrum Duality theory Computations Norm and transfer maps References Index.

Erscheint lt. Verlag 1.4.2008
Reihe/Serie Memoirs of the American Mathematical Society
Verlagsort Providence
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 0-8218-4076-2 / 0821840762
ISBN-13 978-0-8218-4076-4 / 9780821840764
Zustand Neuware
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