Euler systems / / by Karl Rubin

• Autore: Rubin Karl
• Pubblicazione: Princeton, New Jersey ; ; Chichester, England : , : Princeton University Press, , 2000; ©2000
• Descrizione fisica: 1 online resource (241 p.)
• Disciplina: 512/.74
• 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
• Persona (resp. second.): RubinKarl
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• 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
• Sommario/riassunto: 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 1980's in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations. The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry.
• Titolo autorizzato: Euler systems
• ISBN: 0-691-05075-9; 1-4008-6520-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910786510103321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; Number 147.