Serre's conjecture:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1978
|
| Series: | Lecture notes in mathematics
635 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 227 S. |
| ISBN: | 3540086579 0387086579 |
Staff View
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| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1978 | |
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Record in the Search Index
| _version_ | 1804116700644245504 |
|---|---|
| adam_text | Table of Contents
PREFACE
WTR0VUCT10N
CHAPTER 0, JE. FOUNPATIONS
Section 1. Projective modules 1
Section 2. Fiat modules, faithfully flat modules and
finitely presented modules 5
Section 3. Local-global methods 14
Section h. Stably free modules 23
Section 5- Elementary transformations 34
Section 6. The Grothendieck group K 39
Kotes on Chapter One 43
CHAPTER TWO. THE CLASSICAL RESULTS ON SERRE S CÖMJECTURE
Section 1. The case of rank 1 projectives 45
Section 2. The case of one variable 47
Section 3. The case of non-commutative base rings 49
Section 1*. The graded case 55
Section 5. The stable case 59
Section 6. The case of two variables 67
Section 7. The case of big rank 72
Notes on Chapter Two 77
CHAPTER THREE. TWO ELEMENTARE PROOFS OF SERRE S CONJECTURE
Section 1. Susiin s elementary proof 79
Section 2. Vaserstein s elementary proof 85
Section 3. Suslin s monic polynomial theorem 91
Notes on Chapter Three 95
CHAPTER FOUR. HORROCKS THEOREM
Section 1. Localization at monic polynomials 97
Section 2. Statement of Horrocks Theorem 102
Section 3. Swan s proof of Horrocks Theorem 106
Section U. Roberts proof of Horrocks Theorem 114
Section 5• Murthy-Horrocks Theorem 117
Hotes on Chapter Four 121
CHAPTER FII/E. QUILLBH S METHOO
Section 1. Quillen s Patching Theorem 123
Section 2. Affine Horrocks1 Theorem and applications 130
Section 3. Quillen induction, and the Bass-Quillen Conjecture .. 137
Section U. Laurent polynomial rings 143
Section 5• Power series rings 150
Notes on Chapter Five 163
CHAPTER SIX. THE QUAVKAT1C ANALOGUE OF SERRE S CONJECTURE
Section 1. Inner product Spaces l67
Section 2. Karoubi s Theorem 176
Section 3. Härder s Theorem 180
Section h. Parimala s counter-examples 188
Section 5¦ Symplectic Spaces 199
Notes on Chapter Six 203
APPENPIX OW COMPLETE IWTERSECTIONS 205
REFEREUCES 218
LIST OF WOTATIONS 224
INDEX 225
|
| any_adam_object | 1 |
| author | Lam, Tsit-Yuen |
| author_facet | Lam, Tsit-Yuen |
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| author_sort | Lam, Tsit-Yuen |
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| ctrlnum | (OCoLC)605205908 (DE-599)BVBBV002244626 |
| dewey-full | 512/.4 510/.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 510 - Mathematics |
| dewey-raw | 512/.4 510/.8 |
| dewey-search | 512/.4 510/.8 |
| dewey-sort | 3512 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002244626 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:41Z |
| institution | BVB |
| isbn | 3540086579 0387086579 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001475133 |
| oclc_num | 605205908 |
| open_access_boolean | |
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| physical | XV, 227 S. |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Lam, Tsit-Yuen Verfasser aut Serre's conjecture T. Y. Lam Berlin [u.a.] Springer 1978 XV, 227 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 635 Anneaux commutatifs Commutatieve ringen gtt Corps algébriques Lichamen (wiskunde) gtt Modules projectifs (Algèbre) Algebraic fields Commutative rings Projective modules (Algebra) Algebraischer Körper (DE-588)4141852-9 gnd rswk-swf Serre-Vermutung (DE-588)4181056-9 gnd rswk-swf Körpertheorie (DE-588)4164455-4 gnd rswk-swf Kommutativer Ring (DE-588)4164825-0 gnd rswk-swf Serre-Vermutung (DE-588)4181056-9 s DE-604 Körpertheorie (DE-588)4164455-4 s Kommutativer Ring (DE-588)4164825-0 s Algebraischer Körper (DE-588)4141852-9 s Lecture notes in mathematics 635 (DE-604)BV000676446 635 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001475133&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lam, Tsit-Yuen Serre's conjecture Lecture notes in mathematics Anneaux commutatifs Commutatieve ringen gtt Corps algébriques Lichamen (wiskunde) gtt Modules projectifs (Algèbre) Algebraic fields Commutative rings Projective modules (Algebra) Algebraischer Körper (DE-588)4141852-9 gnd Serre-Vermutung (DE-588)4181056-9 gnd Körpertheorie (DE-588)4164455-4 gnd Kommutativer Ring (DE-588)4164825-0 gnd |
| subject_GND | (DE-588)4141852-9 (DE-588)4181056-9 (DE-588)4164455-4 (DE-588)4164825-0 |
| title | Serre's conjecture |
| title_auth | Serre's conjecture |
| title_exact_search | Serre's conjecture |
| title_full | Serre's conjecture T. Y. Lam |
| title_fullStr | Serre's conjecture T. Y. Lam |
| title_full_unstemmed | Serre's conjecture T. Y. Lam |
| title_short | Serre's conjecture |
| title_sort | serre s conjecture |
| topic | Anneaux commutatifs Commutatieve ringen gtt Corps algébriques Lichamen (wiskunde) gtt Modules projectifs (Algèbre) Algebraic fields Commutative rings Projective modules (Algebra) Algebraischer Körper (DE-588)4141852-9 gnd Serre-Vermutung (DE-588)4181056-9 gnd Körpertheorie (DE-588)4164455-4 gnd Kommutativer Ring (DE-588)4164825-0 gnd |
| topic_facet | Anneaux commutatifs Commutatieve ringen Corps algébriques Lichamen (wiskunde) Modules projectifs (Algèbre) Algebraic fields Commutative rings Projective modules (Algebra) Algebraischer Körper Serre-Vermutung Körpertheorie Kommutativer Ring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001475133&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT lamtsityuen serresconjecture |