Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups
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| Autore: |
Rognes John
|
| Titolo: |
Galois Extensions of Structured Ring Spectra/Stably Dualizable Groups
|
| Pubblicazione: | Providence, : American Mathematical Society, 2008 |
| Edizione: | 1st ed. |
| Descrizione fisica: | 1 online resource (154 p.) |
| Disciplina: | 512/.32 |
| Soggetto topico: | Commutative algebra |
| Galois theory | |
| Homology theory | |
| Homotopy theory | |
| Ring extensions (Algebra) | |
| Mathematics | |
| Physical Sciences & Mathematics | |
| Algebra | |
| Note generali: | Description based upon print version of record. |
| Nota di bibliografia: | Includes bibliographical references (p. 131-132) and index. |
| Nota di contenuto: | ""Contents""; ""Galois Extensions of Structured Ring Spectra""; ""Abstract""; ""Chapter 1. Introduction""; ""Chapter 2. Galois extensions in algebra""; ""Â2.1. Galois extensions of fields""; ""Â2.2. Regular covering spaces""; ""Â2.3. Galois extensions of commutative rings""; ""Chapter 3. Closed categories of structured module spectra""; ""Â3.1. Structured spectra""; ""Â3.2. Localized categories""; ""Â3.3. Dualizable spectra""; ""Â3.4. Stably dualizable groups""; ""Â3.5. The dualizing spectrum""; ""Â3.6. The norm map""; ""Chapter 4. Galois extensions in topology"" |
| ""Â4.1. Galois extensions of E-local commutative S-algebras""""Â4.2. The Eilenberg-Mac Lane embedding""; ""Â4.3. Faithful extensions""; ""Chapter 5. Examples of Galois extensions""; ""Â5.1. Trivial extensions""; ""Â5.2. Eilenberg-Mac Lane spectra""; ""Â5.3. Real and complex topological K-theory""; ""Â5.4. The Morava change-of-rings theorem ""; ""Â5.5. The K(1)-local case ""; ""Â5.6. Cochain S-algebras ""; ""Chapter 6. Dualizability and alternate characterizations""; ""Â6.1. Extended equivalences""; ""Â6.2. Dualizability""; ""Â6.3. Alternate characterizations"" | |
| ""Chapter 10. Mapping spaces of commutative S-algebras""""Â10.1. Obstruction theory""; ""Â10.2. Idempotents and connected S-algebras""; ""Â10.3. Separable closure""; ""Chapter 11. Galois theory II""; ""Â11.1. Recovering the Galois group""; ""Â11.2. The brave new Galois correspondence""; ""Chapter 12. Hopfâ€?Galois extensions in topology""; ""Â12.1. Hopfâ€?Galois extensions of commutative S-algebras""; ""Â12.2. Complex cobordism""; ""References""; ""Stably Dualizable Groups""; ""Abstract""; ""Chapter 1. Introduction""; ""Â1.1. The symmetry groups of stable homotopy theory"" | |
| ""Â4.3. Eilenberg-Mac Lane spaces"" | |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Galois Extensions of Structured Ring Spectra |
| ISBN: | 1-4704-0504-0 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910961889103321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Memoirs of the American Mathematical Society