Almost ring theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2003
|
| Schriftenreihe: | Lecture notes in mathematics
1800 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 307 S. |
| ISBN: | 3540405941 |
Internformat
MARC
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| 300 | |a VI, 307 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1800 | |
| 650 | 4 | |a Fastring - Kommutative Algebra - Kategorientheorie | |
| 650 | 4 | |a Arithmetical algebraic geometry | |
| 650 | 4 | |a Categories (Mathematics) | |
| 650 | 4 | |a Commutative rings | |
| 650 | 4 | |a Valuation theory | |
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| 650 | 0 | 7 | |a Kommutative Algebra |0 (DE-588)4164821-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kategorientheorie |0 (DE-588)4120552-2 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-010441273 | ||
Datensatz im Suchindex
| _version_ | 1804130160168927232 |
|---|---|
| adam_text | Contents
1. Introduction 1
1.1. Motivations and a little history 1
1.2. The method of almost etale extensions 3
1.3. Contents of this book 7
1.4. The view from above 9
1.5. Acknowledgements 10
2. Homological theory 11
2.1. Some ring theoretic preliminaries 11
2.2. Categories of almost modules and algebras 16
2.3. Uniform spaces of almost modules 23
2.4. Almost homological algebra 31
2.5. Almost homotopical algebra 40
3. Almost ring theory 50
3.1. Flat, unramified and etale morphisms 51
3.2. Nilpotent deformations of almost algebras and modules 53
3.3. Nilpotent deformations of torsors 61
3.4. Descent 71
3.5. Behaviour of etale morphisms under Frobenius 82
4. Fine study of almost projective modules 92
4.1. Almost traces 92
4.2. Endomorphisms of Gm. 100
4.3. Modules of almost finite rank 107
4.4. Localization in the flat site 113
4.5. Construction of quotients by flat equivalence relations 123
5. Henselization and completion of almost algebras 130
5.1. Henselian pairs 131
5.2. Criteria for unramified morphisms 135
5.3. Topological algebras and modules 141
5.4. Henselian approximation of structures over adically complete rings 148
5.5. Lifting theorems for henselian pairs 162
5.6. Smooth locus of an affine almost scheme 171
5.7. Quasi projective almost schemes 180
5.8. Lifting and descent of torsors 189
6. Valuation theory 195
6.1. Ordered groups and valuations 196
6.2. Basic ramification theory 206
6.3. Algebraic extensions 210
6.4. Logarithmic differentials 220
6.5. Transcendental extensions 226
6.6. Deeply ramified extensions 234
7. Analytic geometry 242
7.1. Derived completion functor 243
7.2. Cotangent complex for formal schemes and adic spaces 251
vi Contents
7.3. Deformations of formal schemes and adic spaces 262
7.4. Analytic geometry over a deeply ramified base 272
7.5. Semicontinuity of the discriminant 278
8. Appendix 287
8.1. Simplicial almost algebras 287
8.2. Fundamental group of an almost algebra 292
References 301
Index 304
|
| any_adam_object | 1 |
| author | Gabber, Ofer 1958- Ramero, Lorenzo |
| author_GND | (DE-588)124938922 |
| author_facet | Gabber, Ofer 1958- Ramero, Lorenzo |
| author_role | aut aut |
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| author_variant | o g og l r lr |
| building | Verbundindex |
| bvnumber | BV017321122 |
| callnumber-first | Q - Science |
| callnumber-label | QA251 |
| callnumber-raw | QA251.3 QA3.L28 no. 1800 |
| callnumber-search | QA251.3 QA3.L28 no. 1800 |
| callnumber-sort | QA 3251.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 SK 230 |
| ctrlnum | (OCoLC)249200824 (DE-599)BVBBV017321122 |
| dewey-full | 512.44 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 510 - Mathematics |
| dewey-raw | 512.44 510 |
| dewey-search | 512.44 510 |
| dewey-sort | 3512.44 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV017321122 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:16:37Z |
| institution | BVB |
| isbn | 3540405941 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010441273 |
| oclc_num | 249200824 |
| open_access_boolean | |
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| physical | VI, 307 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Gabber, Ofer 1958- Verfasser (DE-588)124938922 aut Almost ring theory Ofer Gabber ; Lorenzo Ramero Berlin [u.a.] Springer 2003 VI, 307 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1800 Fastring - Kommutative Algebra - Kategorientheorie Arithmetical algebraic geometry Categories (Mathematics) Commutative rings Valuation theory Fastring (DE-588)4192482-4 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Fastring (DE-588)4192482-4 s Kommutative Algebra (DE-588)4164821-3 s Kategorientheorie (DE-588)4120552-2 s DE-604 Ramero, Lorenzo Verfasser aut Lecture notes in mathematics 1800 (DE-604)BV000676446 1800 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441273&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gabber, Ofer 1958- Ramero, Lorenzo Almost ring theory Lecture notes in mathematics Fastring - Kommutative Algebra - Kategorientheorie Arithmetical algebraic geometry Categories (Mathematics) Commutative rings Valuation theory Fastring (DE-588)4192482-4 gnd Kommutative Algebra (DE-588)4164821-3 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| subject_GND | (DE-588)4192482-4 (DE-588)4164821-3 (DE-588)4120552-2 |
| title | Almost ring theory |
| title_auth | Almost ring theory |
| title_exact_search | Almost ring theory |
| title_full | Almost ring theory Ofer Gabber ; Lorenzo Ramero |
| title_fullStr | Almost ring theory Ofer Gabber ; Lorenzo Ramero |
| title_full_unstemmed | Almost ring theory Ofer Gabber ; Lorenzo Ramero |
| title_short | Almost ring theory |
| title_sort | almost ring theory |
| topic | Fastring - Kommutative Algebra - Kategorientheorie Arithmetical algebraic geometry Categories (Mathematics) Commutative rings Valuation theory Fastring (DE-588)4192482-4 gnd Kommutative Algebra (DE-588)4164821-3 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| topic_facet | Fastring - Kommutative Algebra - Kategorientheorie Arithmetical algebraic geometry Categories (Mathematics) Commutative rings Valuation theory Fastring Kommutative Algebra Kategorientheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441273&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT gabberofer almostringtheory AT ramerolorenzo almostringtheory |