Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups.

Intro -- Contents -- Galois Extensions of Structured Ring Spectra -- Abstract -- Chapter 1. Introduction -- Chapter 2. Galois extensions in algebra -- 2.1. Galois extensions of fields -- 2.2. Regular covering spaces -- 2.3. Galois extensions of commutative rings -- Chapter 3. Closed categories of structured module spectra -- 3.1. Structured spectra -- 3.2. Localized categories -- 3.3. Dualizable spectra -- 3.4. Stably dualizable groups -- 3.5. The dualizing spectrum -- 3.6. The norm map -- Chapter 4. Galois extensions in topology -- 4.1. Galois extensions of E-local commutative S-algebras -- 4.2. The Eilenberg-Mac Lane embedding -- 4.3. Faithful extensions -- Chapter 5. Examples of Galois extensions -- 5.1. Trivial extensions -- 5.2. Eilenberg-Mac Lane spectra -- 5.3. Real and complex topological K-theory -- 5.4. The Morava change-of-rings theorem -- 5.5. The K(1)-local case -- 5.6. Cochain S-algebras -- Chapter 6. Dualizability and alternate characterizations -- 6.1. Extended equivalences -- 6.2. Dualizability -- 6.3. Alternate characterizations -- 6.4. The trace map and self-duality -- 6.5. Smash invertible modules -- Chapter 7. Galois theory I -- 7.1. Base change for Galois extensions -- 7.2. Fixed S-algebras -- Chapter 8. Pro-Galois extensions and the Amitsur complex -- 8.1. Pro-Galois extensions -- 8.2. The Amitsur complex -- Chapter 9. Separable and étale extensions -- 9.1. Separable extensions -- 9.2. Symmetrically étale extensions -- 9.3. Smashing maps -- 9.4. Étale extensions -- 9.5. Henselian maps -- 9.6. I-adic towers -- Chapter 10. Mapping spaces of commutative S-algebras -- 10.1. Obstruction theory -- 10.2. Idempotents and connected S-algebras -- 10.3. Separable closure -- Chapter 11. Galois theory II -- 11.1. Recovering the Galois group -- 11.2. The brave new Galois correspondence.

Chapter 12. Hopf-Galois extensions in topology -- 12.1. Hopf-Galois extensions of commutative S-algebras -- 12.2. Complex cobordism -- References -- Stably Dualizable Groups -- Abstract -- Chapter 1. Introduction -- 1.1. The symmetry groups of stable homotopy theory -- 1.2. Algebraic localizations and completions -- 1.3. Chromatic localizations and completions -- 1.4. Applications -- Chapter 2. The dualizing spectrum -- 2.1. The E-local stable category -- 2.2. Dualizable spectra -- 2.3. Stably dualizable groups -- 2.4. E-compact groups -- 2.5. The dualizing and inverse dualizing spectra -- Chapter 3. Duality theory -- 3.1. Poincaré duality -- 3.2. Inverse Poincare duality -- 3.3. The Picard group -- Chapter 4. Computations -- 4.1. A spectral sequence for E-homology -- 4.2. Morava K-theories -- 4.3. Eilenberg-Mac Lane spaces -- Chapter 5. Norm and transfer maps -- 5.1. Thom spectra -- 5.2. The norm map and Tate cohomology -- 5.3. The G-transfer map -- 5.4. E-local homotopy classes -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Y -- Z.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.