Kolyvagin systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2004
|
| Series: | Memoirs of the American Mathematical Society
799 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 168, Number 799 (end of volume) Includes bibliographical references |
| Physical Description: | VII, 96 S. |
| ISBN: | 0821835122 9780821835128 |
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| 300 | |a VII, 96 S. | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 799 | |
| 500 | |a Volume 168, Number 799 (end of volume) | ||
| 500 | |a Includes bibliographical references | ||
| 650 | 7 | |a Galois-theorie |2 gtt | |
| 650 | 7 | |a Geometria algébrica |2 larpcal | |
| 650 | 7 | |a L-functies |2 gtt | |
| 650 | 7 | |a Teoria dos números |2 larpcal | |
| 650 | 4 | |a Arithmetical algebraic geometry | |
| 650 | 4 | |a Birch-Swinnerton-Dyer conjecture | |
| 650 | 4 | |a L-functions | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction 1
0.1. Selmer sheaves and Kolyvagin systems 1
0.2. Resemblance to the leading term of an L function 2
0.3. Applications 3
0.4. Layout of the paper 4
0.5. Notation 5
0.6. Acknowledgments 5
Chapter 1. Local Cohomology Groups 7
1.1. Local conditions 7
1.2. The finite/singular homomorphism 10
1.3. Local duality 11
Chapter 2. Global Cohomology Groups and Selmer Structures 13
2.1. Selmer modules 13
2.2. Comparing Selmer modules 16
2.3. Global duality 16
Chapter 3. Kolyvagin Systems 19
3.1. Kolyvagin systems 19
3.2. Euler systems and Kolyvagin systems 23
3.3. Simplicial sheaves and Selmer groups 24
3.4. Sheaves and monodromy 26
3.5. Hypotheses on T, T, and V 27
3.6. Choosing useful primes 30
3.7. Some remarks about hypothesis (H.6) 33
Chapter 4. Kolyvagin Systems over Principal Artinian Rings 35
4.1. The core Selmer module 35
4.2. Kolyvagin systems and the core rank 40
4.3. The sheaf of stub Selmer modules 41
4.4. Kolyvagin systems and the stub Selmer sheaf 45
4.5. Kolyvagin systems over principal artinian rings 48
Chapter 5. Kolyvagin Systems over Integral Domains 55
5.1. Kolyvagin systems over a field 55
5.2. Kolyvagin systems over a discrete valuation ring 56
5.3. Kolyvagin systems over A 60
Chapter 6. Examples 69
6.1. The multiplicative group 69
V
vi CONTENTS
6.2. Elliptic curves 73
6.3. The multiplicative group, revisited 76
Appendix A. Proof of Theorem 3.2.4 79
Appendix B. Proof of Theorem 4.3.3, by Benjamin Howard 89
Bibliography 95
|
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| id | DE-604.BV017732717 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:21:17Z |
| institution | BVB |
| isbn | 0821835122 9780821835128 |
| language | English |
| lccn | 2003066064 |
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| physical | VII, 96 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
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| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Mazur, Barry 1937- Verfasser (DE-588)107715945 aut Kolyvagin systems Barry Mazur ; Karl Rubin Providence, R.I. American Mathematical Society 2004 VII, 96 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 799 Volume 168, Number 799 (end of volume) Includes bibliographical references Galois-theorie gtt Geometria algébrica larpcal L-functies gtt Teoria dos números larpcal Arithmetical algebraic geometry Birch-Swinnerton-Dyer conjecture L-functions Arithmetische Geometrie (DE-588)4131383-5 gnd rswk-swf L-Funktion (DE-588)4137026-0 gnd rswk-swf L-Funktion (DE-588)4137026-0 s Arithmetische Geometrie (DE-588)4131383-5 s DE-604 Rubin, Karl Sonstige oth Memoirs of the American Mathematical Society 799 (DE-604)BV008000141 799 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010657904&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mazur, Barry 1937- Kolyvagin systems Memoirs of the American Mathematical Society Galois-theorie gtt Geometria algébrica larpcal L-functies gtt Teoria dos números larpcal Arithmetical algebraic geometry Birch-Swinnerton-Dyer conjecture L-functions Arithmetische Geometrie (DE-588)4131383-5 gnd L-Funktion (DE-588)4137026-0 gnd |
| subject_GND | (DE-588)4131383-5 (DE-588)4137026-0 |
| title | Kolyvagin systems |
| title_auth | Kolyvagin systems |
| title_exact_search | Kolyvagin systems |
| title_full | Kolyvagin systems Barry Mazur ; Karl Rubin |
| title_fullStr | Kolyvagin systems Barry Mazur ; Karl Rubin |
| title_full_unstemmed | Kolyvagin systems Barry Mazur ; Karl Rubin |
| title_short | Kolyvagin systems |
| title_sort | kolyvagin systems |
| topic | Galois-theorie gtt Geometria algébrica larpcal L-functies gtt Teoria dos números larpcal Arithmetical algebraic geometry Birch-Swinnerton-Dyer conjecture L-functions Arithmetische Geometrie (DE-588)4131383-5 gnd L-Funktion (DE-588)4137026-0 gnd |
| topic_facet | Galois-theorie Geometria algébrica L-functies Teoria dos números Arithmetical algebraic geometry Birch-Swinnerton-Dyer conjecture L-functions Arithmetische Geometrie L-Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010657904&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT mazurbarry kolyvaginsystems AT rubinkarl kolyvaginsystems |