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Euler systems / / by Karl Rubin
| Euler systems / / by Karl Rubin |
| Autore | Rubin Karl |
| Pubbl/distr/stampa | Princeton, New Jersey ; ; Chichester, England : , : Princeton University Press, , 2000 |
| Descrizione fisica | 1 online resource (241 p.) |
| Disciplina | 512/.74 |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Algebraic number theory
p-adic numbers |
| Soggetto genere / forma | Electronic books. |
| ISBN |
0-691-05075-9
1-4008-6520-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Acknowledgments / Rubin, Karl -- Introduction -- Chapter 1. Galois Cohomology of p-adic Representations -- Chapter 2. Euler Systems: Definition and Main Results -- Chapter 3. Examples and Applications -- Chapter 4. Derived Cohomology Classes -- Chapter 5. Bounding the Selmer Group -- Chapter 6. Twisting -- Chapter 7. Iwasawa Theory -- Chapter 8. Euler Systems and p-adic L-functions -- Chapter 9. Variants -- Appendix A. Linear Algebra -- Appendix B. Continuous Cohomology and Inverse Limits -- Appendix C. Cohomology of p-adic Analytic Groups -- Appendix D. p-adic Calculations in Cyclotomic Fields -- Bibliography -- Index of Symbols -- Subject Index |
| Record Nr. | UNINA-9910465328803321 |
Rubin Karl
|
||
| Princeton, New Jersey ; ; Chichester, England : , : Princeton University Press, , 2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Euler systems / / by Karl Rubin
| Euler systems / / by Karl Rubin |
| Autore | Rubin Karl |
| Pubbl/distr/stampa | Princeton, New Jersey ; ; Chichester, England : , : Princeton University Press, , 2000 |
| Descrizione fisica | 1 online resource (241 p.) |
| Disciplina | 512/.74 |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Algebraic number theory
p-adic numbers |
| Soggetto non controllato |
Abelian extension
Abelian variety Absolute Galois group Algebraic closure Barry Mazur Big O notation Birch and Swinnerton-Dyer conjecture Cardinality Class field theory Coefficient Cohomology Complex multiplication Conjecture Corollary Cyclotomic field Dimension (vector space) Divisibility rule Eigenvalues and eigenvectors Elliptic curve Error term Euler product Euler system Exact sequence Existential quantification Field of fractions Finite set Functional equation Galois cohomology Galois group Galois module Gauss sum Global field Heegner point Ideal class group Integer Inverse limit Inverse system Karl Rubin Local field Mathematical induction Maximal ideal Modular curve Modular elliptic curve Natural number Orthogonality P-adic number Pairing Principal ideal R-factor (crystallography) Ralph Greenberg Remainder Residue field Ring of integers Scientific notation Selmer group Subgroup Tate module Taylor series Tensor product Theorem Upper and lower bounds Victor Kolyvagin |
| ISBN |
0-691-05075-9
1-4008-6520-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Acknowledgments / Rubin, Karl -- Introduction -- Chapter 1. Galois Cohomology of p-adic Representations -- Chapter 2. Euler Systems: Definition and Main Results -- Chapter 3. Examples and Applications -- Chapter 4. Derived Cohomology Classes -- Chapter 5. Bounding the Selmer Group -- Chapter 6. Twisting -- Chapter 7. Iwasawa Theory -- Chapter 8. Euler Systems and p-adic L-functions -- Chapter 9. Variants -- Appendix A. Linear Algebra -- Appendix B. Continuous Cohomology and Inverse Limits -- Appendix C. Cohomology of p-adic Analytic Groups -- Appendix D. p-adic Calculations in Cyclotomic Fields -- Bibliography -- Index of Symbols -- Subject Index |
| Record Nr. | UNINA-9910786510103321 |
|
Rubin Karl
|
||
| Princeton, New Jersey ; ; Chichester, England : , : Princeton University Press, , 2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Euler systems / / by Karl Rubin
| Euler systems / / by Karl Rubin |
| Autore | Rubin Karl |
| Pubbl/distr/stampa | Princeton, New Jersey ; ; Chichester, England : , : Princeton University Press, , 2000 |
| Descrizione fisica | 1 online resource (241 p.) |
| Disciplina | 512/.74 |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Algebraic number theory
p-adic numbers |
| Soggetto non controllato |
Abelian extension
Abelian variety Absolute Galois group Algebraic closure Barry Mazur Big O notation Birch and Swinnerton-Dyer conjecture Cardinality Class field theory Coefficient Cohomology Complex multiplication Conjecture Corollary Cyclotomic field Dimension (vector space) Divisibility rule Eigenvalues and eigenvectors Elliptic curve Error term Euler product Euler system Exact sequence Existential quantification Field of fractions Finite set Functional equation Galois cohomology Galois group Galois module Gauss sum Global field Heegner point Ideal class group Integer Inverse limit Inverse system Karl Rubin Local field Mathematical induction Maximal ideal Modular curve Modular elliptic curve Natural number Orthogonality P-adic number Pairing Principal ideal R-factor (crystallography) Ralph Greenberg Remainder Residue field Ring of integers Scientific notation Selmer group Subgroup Tate module Taylor series Tensor product Theorem Upper and lower bounds Victor Kolyvagin |
| ISBN |
0-691-05075-9
1-4008-6520-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Acknowledgments / Rubin, Karl -- Introduction -- Chapter 1. Galois Cohomology of p-adic Representations -- Chapter 2. Euler Systems: Definition and Main Results -- Chapter 3. Examples and Applications -- Chapter 4. Derived Cohomology Classes -- Chapter 5. Bounding the Selmer Group -- Chapter 6. Twisting -- Chapter 7. Iwasawa Theory -- Chapter 8. Euler Systems and p-adic L-functions -- Chapter 9. Variants -- Appendix A. Linear Algebra -- Appendix B. Continuous Cohomology and Inverse Limits -- Appendix C. Cohomology of p-adic Analytic Groups -- Appendix D. p-adic Calculations in Cyclotomic Fields -- Bibliography -- Index of Symbols -- Subject Index |
| Record Nr. | UNINA-9910816804403321 |
|
Rubin Karl
|
||
| Princeton, New Jersey ; ; Chichester, England : , : Princeton University Press, , 2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Kolyvagin systems / / Barry Mazur, Karl Rubin
| Kolyvagin systems / / Barry Mazur, Karl Rubin |
| Autore | Mazur Barry |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (112 p.) |
| Disciplina | 516.3/5 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Birch-Swinnerton-Dyer conjecture
L-functions Arithmetical algebraic geometry |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0397-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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 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"" |
| Record Nr. | UNINA-9910478885603321 |
|
Mazur Barry
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Kolyvagin systems / / Barry Mazur, Karl Rubin
| Kolyvagin systems / / Barry Mazur, Karl Rubin |
| Autore | Mazur Barry |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (112 p.) |
| Disciplina | 516.3/5 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Birch-Swinnerton-Dyer conjecture
L-functions Arithmetical algebraic geometry |
| ISBN | 1-4704-0397-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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 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"" |
| Record Nr. | UNINA-9910788746203321 |
|
Mazur Barry
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Kolyvagin systems / / Barry Mazur, Karl Rubin
| Kolyvagin systems / / Barry Mazur, Karl Rubin |
| Autore | Mazur Barry |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (112 p.) |
| Disciplina | 516.3/5 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Birch-Swinnerton-Dyer conjecture
L-functions Arithmetical algebraic geometry |
| ISBN | 1-4704-0397-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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 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"" |
| Record Nr. | UNINA-9910813658303321 |
|
Mazur Barry
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||