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Record Nr. |
UNINA9910478885603321 |
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Autore |
Mazur Barry |
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Titolo |
Kolyvagin systems / / Barry Mazur, Karl Rubin |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 2004 |
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©2004 |
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ISBN |
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Descrizione fisica |
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1 online resource (112 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 168, Number 799 |
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Disciplina |
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Soggetti |
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Birch-Swinnerton-Dyer conjecture |
L-functions |
Arithmetical algebraic geometry |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"March 2004, Volume 168, Number 799 (end of volume)." |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""Contents""; ""Introduction""; ""0.1. Selmer sheaves and Kolyvagin systems""; ""0.2. Resemblance to the leading term of an L-function""; ""0.3. Applications""; ""0.4. Layout of the paper""; ""0.5. Notation""; ""0.6. Acknowledgments""; ""Chapter 1. Local Cohomology Groups""; ""1.1. Local conditions""; ""1.2. The finite/singular homomorphism""; ""1.3. Local duality""; ""Chapter 2. Global Cohomology Groups and Selmer Structures""; ""2.1. Selmer modules""; ""2.2. Comparing Selmer modules""; ""2.3. Global duality""; ""Chapter 3. Kolyvagin Systems""; ""3.1. Kolyvagin systems"" |
""3.2. Euler systems and Kolyvagin systems""""3.3. Simplicial sheaves and Selmer groups""; ""3.4. Sheaves and monodromy""; ""3.5. Hypotheses on T,F, and p""; ""3.6. Choosing useful primes""; ""3.7. Some remarks about hypothesis ( H.6)""; ""Chapter 4. Kolyvagin Systems over Principal Artinian Rings""; ""4.1. The core Selmer module""; ""4.2. Kolyvagin systems and the core rank""; ""4.3. The sheaf of stub Selmer modules""; ""4.4. Kolyvagin systems and the stub Selmer sheaf""; ""4.5. Kolyvagin systems over principal artinian rings""; ""Chapter 5. Kolyvagin Systems over Integral Domains"" |
""5.1. Kolyvagin systems over a field""""5.2. Kolyvagin systems over a |
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discrete valuation ring""; ""5.3. Kolyvagin systems over A""; ""Chapter 6. Examples""; ""6.1. The multiplicative group""; ""6.2. Elliptic curves""; ""6.3. The multiplicative group, revisited""; ""Appendix A. Proof of Theorem 3.2.4""; ""Appendix B. Proof of Theorem 4.3.3""; ""Bibliography"" |
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