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Catalogue Information
Field name	Details
Dewey Class	512.7
Title	Arithmetic of p-adic Modular Forms ([EBook]) / by Fernando Quadros Gouvêa.
Author	Gouvêa, Fernando Q. (Fernando Quadros) , 1957-
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 1988.
Physical Details	X, 122 pages : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1304
ISBN	9783540388548
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0082111
Links to Related Works	Subject References: Algebraic Geometry . Forms, Modular . Modular Forms . Modules (Algebra) . Number Theory . p-adic analysis . Authors: Gouvêa, Fernando Q. (Fernando Quadros) 1957- . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 512.7 .

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Arithmetic of p-adic Modular Forms

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