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Record Nr. |
UNINA9910495183803321 |
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Autore |
Bellaïche Joël |
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Titolo |
The Eigenbook : Eigenvarieties, families of Galois representations, p-adic L-functions / / Joël Bellaïche |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Birkhäuser, , [2021] |
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©2021 |
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ISBN |
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Edizione |
[1st ed. 2021.] |
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Descrizione fisica |
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1 online resource (XI, 316 p. 16 illus., 1 illus. in color.) |
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Collana |
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Pathways in mathematics, , 2367-3451 |
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Disciplina |
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Soggetti |
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Number theory |
Teoria de nombres |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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- Introduction -- Part I The ‘Eigen’ Construction -- Eigenalgebras -- Eigenvarieties -- Part II Modular Symbols and L-Functions -- Abstract Modular Symbols -- Classical Modular Symbols, Modular Forms, L-functions -- Rigid Analytic Modular Symbols and p-Adic L-functions -- Part III The Eigencurve and its p-Adic L-Functions -- The Eigencurve of Modular Symbols -- p-Adic L-Functions on the Eigencurve -- The Adjoint p-Adic L-Function and the Ramification Locus of the Eigencurve -- Solutions and Hints to Exercises. |
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Sommario/riassunto |
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This book discusses the p-adic modular forms, the eigencurve that parameterize them, and the p-adic L-functions one can associate to them. These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory. For graduate students and newcomers to this field, the book provides a solid introduction to this highly active area of research. For experts, it will offer the convenience of collecting into one place foundational definitions and theorems with complete and self-contained proofs. Written in an engaging and educational style, the book also includes exercises and provides their solution. |
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