Galois extensions of structured ring spectra: stably dualizable groups
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, RI
Am. Math. Soc.
2008
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
898 = 192,3 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020114716&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S. 131 - 132 |
| Umfang: | VII, 137 S. graph. Darst. |
| ISBN: | 9780821840764 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Galois Extensions of Structured Ring Spectra 1
Abstract 2
Chapter 1. Introduction 3
Chapter 2. Galois extensions in algebra ]()
§2.1. Galois extensions of fields 10
§2.2. Regular covering spaces 10
§2.3. Galois extensions of commutative rings 11
Chapter 3. Closed categories of structured module spectra 14
§3.1. Structured spectra 14
§3.2. Localized categories 15
§3.3. Dualizable spectra 17
§3.4. Stably dualizable groups 18
§3.5. The dualizing spectrum 19
§3.6. The norm map 20
Chapter 4. Galois extensions in topology 21
§4.1. Galois extensions of E-local commutative S-algebras 21
§4.2. The Eilenberg~Mac Lane embedding 22
§4.3. Faithful extensions 23
Chapter 5. Examples of Galois extensions 2. i
§5.1. Trivial extensions 2-r)
§5.2. Eilenberg- Mac Lane spectra 25
§5.3. Real and complex topological A*-theory 25
§5.4. The Morava change-of-rings theorem 27
§5.5. The A (l)-local case 34
§5.6. Cochain S-algebras 37
Chapter 6. Dualizability and alternate characterizations 40
§6.1. Extended equivalences 40
§6.2. Dualizability 41
§6.3. Alternate characterizations 45
§6.4. The trace map and self-duality 46
§6.5. Smash invertible modules 19
Chapter 7. Galois theory I 51
§7.1. Base change for Galois extensions 51
v
vi CONTENTS
§7.2. Fixed 5-algebras 52
Chapter 8. Pro-Galois extensions and the Amitsur complex 56
§8.1. Pro-Galois extensions 56
§8.2. The Amitsur complex 57
Chapter 9. Separable and etale extensions 61
§9.1. Separable extensions 61
§9.2. Symmetrically etale extensions 63
§9.3. Smashing maps 65
§9.4. Etale extensions 66
§9.5. Henselian maps 68
§9.6. 7-adic towers 72
Chapter 10. Mapping spaces of commutative S-algebras 77
§10.1. Obstruction theory 77
§10.2. Idempotents and connected 5-algebras 80
§10.3. Separable closure 82
Chapter 11. Galois theory II 85
§11.1. Recovering the Galois group 85
§11.2. The brave new Galois correspondence 86
Chapter 12. Hopf-Galois extensions in topology 89
§12.1. Hopf-Galois extensions of commutative ^-algebras 89
§12.2. Complex cobordism 91
References 94
Stably Dualizable Groups 99
Abstract 100
Chapter 1. Introduction 101
§1.1. The symmetry groups of stable homotopy theory 101
§1.2. Algebraic localizations and completions 101
§1.3. Chromatic localizations and completions 103
§1.4. Applications 104
Chapter 2. The dualizing spectrum 106
§2.1. The £-local stable category 1°6
§2.2. Dualizable spectra 1°7
§2.3. Stably dualizable groups 108
§2.4. B-compact groups 109
§2.5. The dualizing and inverse dualizing spectra HI
Chapter 3. Duality theory H4
§3.1. Poincare duality 114
§3.2. Inverse Poincare duality H6
§3.3. The Picard group I19
Chapter 4. Computations 121
§4.1. A spectral sequence for i?-homology 121
CONTENTS vii
§4.2. Morava K-theories 121
§4.3. Eilenberg-Mac Lane spaces 124
Chapter 5. Norm and transfer maps 126
§5.1. Thorn spectra 126
§5.2. The norm map and Tate cohomology 126
§5.3. The G-transfer map 129
§5.4. E-local homotopy classes 129
References 131
Index 133
|
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV025503496 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:29:24Z |
| institution | BVB |
| isbn | 9780821840764 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020114716 |
| oclc_num | 254488083 |
| open_access_boolean | |
| owner | DE-11 |
| owner_facet | DE-11 |
| physical | VII, 137 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Am. Math. Soc. |
| record_format | marc |
| series2 | Memoirs of the American Mathematical Society |
| spellingShingle | Rognes, John 1966- Galois extensions of structured ring spectra stably dualizable groups Ringspektrum (DE-588)4523143-6 gnd Galois-Erweiterung (DE-588)4155900-9 gnd |
| subject_GND | (DE-588)4523143-6 (DE-588)4155900-9 |
| title | Galois extensions of structured ring spectra stably dualizable groups |
| title_auth | Galois extensions of structured ring spectra stably dualizable groups |
| title_exact_search | Galois extensions of structured ring spectra stably dualizable groups |
| title_full | Galois extensions of structured ring spectra stably dualizable groups John Rognes |
| title_fullStr | Galois extensions of structured ring spectra stably dualizable groups John Rognes |
| title_full_unstemmed | Galois extensions of structured ring spectra stably dualizable groups John Rognes |
| title_short | Galois extensions of structured ring spectra |
| title_sort | galois extensions of structured ring spectra stably dualizable groups |
| title_sub | stably dualizable groups |
| topic | Ringspektrum (DE-588)4523143-6 gnd Galois-Erweiterung (DE-588)4155900-9 gnd |
| topic_facet | Ringspektrum Galois-Erweiterung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020114716&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT rognesjohn galoisextensionsofstructuredringspectrastablydualizablegroups |