Euler systems /

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One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in order to bound...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Rubin, Karl (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, New Jersey ; Chichester, England : Princeton University Press, 2000.
Colección:Annals of mathematics studies ; no. 147.
Temas:
Algebraic number theory.
p-adic numbers.
Théorie algébrique des nombres.
Nombres p-adiques.
MATHEMATICS > Algebra > Intermediate.
MATHEMATICS > Number Theory.
Algebraic number theory
p-adic numbers
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.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Frontmatter
  • 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.

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