Arithmetic of p-adic Modular Forms

GouvĂȘa, Fernando Quadros.

Arithmetic of p-adic Modular Forms [electronic resource] / by Fernando Quadros GouvĂȘa. - X, 122 p. online resource. - Lecture Notes in Mathematics, 1304 0075-8434 ; . - Lecture Notes in Mathematics, 1304 .

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.

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.

9783540388548

10.1007/BFb0082111 doi


Number theory.
Geometry, algebraic.
Number Theory.
Algebraic Geometry.

QA241-247.5

512.7
(C) Powered by Koha

Powered by Koha