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Arithmetic of p-adic Modular Forms

Fernando Q. Gouvea (Autor)

Buch | Softcover

X, 122 Seiten

1988
Springer Berlin (Verlag)
978-3-540-18946-6 (ISBN)

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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: 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.

Erscheint lt. Verlag	23.3.1988
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	X, 122 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	211 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	area • arithmetic • Boundary element method • Duality • Field • Form • Function • Functions • modular form • Operator • presentation • Review • Theorem
ISBN-10	3-540-18946-7 / 3540189467
ISBN-13	978-3-540-18946-6 / 9783540189466
Zustand	Neuware