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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
Opac: Controlla la disponibilità qui
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
Opac: Controlla la disponibilità qui
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
Opac: Controlla la disponibilità qui
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
Opac: Controlla la disponibilità qui
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
Opac: Controlla la disponibilità qui
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
Opac: Controlla la disponibilità qui