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- catalog abstract "The central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of modular forms is assumed known to the reader, but the p-adic theory is reviewed in detail, with ample intuitive and heuristic discussion, so that the book will serve as a convenient point of entry to research in that area. The results on the U operator and on Galois representations are new, and will be of interest even to the experts. A list of further problems in the field is included to guide the beginner in his research. The book will thus be of interest to number theorists who wish to learn about p-adic modular forms, leading them rapidly to interesting research, and also to the specialists in the subject.".
- catalog contributor b2082553.
- catalog created "c1988.".
- catalog date "1988".
- catalog date "c1988.".
- catalog dateCopyrighted "c1988.".
- catalog description "Bibliography: p. [117]-119.".
- catalog description "Contents: p-adic Modular Forms: Level Structures and Trivializations. p-adic Modular Forms with Growth Conditions. Generalized p-adic Modular Functions -- Hecke and U Operators: Hecke Operators. The Frobenius Operator. The U Operator. Appendix: Hida's Theory of the Ordinary Part -- Galois Representations: Duality Theorems. Families of Modular Forms. Changing the Level. Deformations of Residual Eigenforms. Deformations of Galois Representations. The Modular Deformation Space. Further Questions.".
- catalog description "The central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of modular forms is assumed known to the reader, but the p-adic theory is reviewed in detail, with ample intuitive and heuristic discussion, so that the book will serve as a convenient point of entry to research in that area. The results on the U operator and on Galois representations are new, and will be of interest even to the experts. A list of further problems in the field is included to guide the beginner in his research. The book will thus be of interest to number theorists who wish to learn about p-adic modular forms, leading them rapidly to interesting research, and also to the specialists in the subject.".
- catalog extent "viii, 121 p. :".
- catalog identifier "0387189467 (New York)".
- catalog identifier "3540189467 (Berlin)".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1304.".
- catalog isPartOf "Lecture notes in mathematics ; 1304".
- catalog issued "1988".
- catalog issued "c1988.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog subject "Forms, Modular.".
- catalog subject "Geometry, algebraic.".
- catalog subject "Mathematics.".
- catalog subject "Number theory.".
- catalog subject "p-adic analysis.".
- catalog tableOfContents "Contents: p-adic Modular Forms: Level Structures and Trivializations. p-adic Modular Forms with Growth Conditions. Generalized p-adic Modular Functions -- Hecke and U Operators: Hecke Operators. The Frobenius Operator. The U Operator. Appendix: Hida's Theory of the Ordinary Part -- Galois Representations: Duality Theorems. Families of Modular Forms. Changing the Level. Deformations of Residual Eigenforms. Deformations of Galois Representations. The Modular Deformation Space. Further Questions.".
- catalog title "Arithmetic of p-adic modular forms / Fernando Q. Gouvêa.".
- catalog type "text".