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Cover: 9783030772628 | The Eigenbook | Joël Bellaïche | Buch | Pathways in Mathematics | xi
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The Eigenbook
Eigenvarieties, families of Galois representations, p-adic L-functions
Buch von Joël Bellaïche
Sprache: Englisch

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Beschreibung
¿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.
¿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.
Über den Autor
Joël Bellaïche studied at the École Normale Supérieure of Paris and obtained his PhD at the university of Orsay. He is now professor at Brandeis University. His research interest are in Number Theory, Automorphic Forms, Galois Representations, L-functions, and Algebraic Geometry.
Zusammenfassung

Offers a comprehensive and solid introduction to the theory

Includes exercises and solutions

Presents a unique collection of knowledge on this theory not available elsewhere

Inhaltsverzeichnis
- 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.
Details
Erscheinungsjahr: 2021
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Pathways in Mathematics
Inhalt: xi
316 S.
15 s/w Illustr.
1 farbige Illustr.
316 p. 16 illus.
1 illus. in color.
ISBN-13: 9783030772628
ISBN-10: 3030772624
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Bellaïche, Joël
Auflage: 1st ed. 2021
Hersteller: Springer International Publishing
Springer International Publishing AG
Pathways in Mathematics
Maße: 241 x 160 x 24 mm
Von/Mit: Joël Bellaïche
Erscheinungsdatum: 13.08.2021
Gewicht: 0,658 kg
Artikel-ID: 119926853
Über den Autor
Joël Bellaïche studied at the École Normale Supérieure of Paris and obtained his PhD at the university of Orsay. He is now professor at Brandeis University. His research interest are in Number Theory, Automorphic Forms, Galois Representations, L-functions, and Algebraic Geometry.
Zusammenfassung

Offers a comprehensive and solid introduction to the theory

Includes exercises and solutions

Presents a unique collection of knowledge on this theory not available elsewhere

Inhaltsverzeichnis
- 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.
Details
Erscheinungsjahr: 2021
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Pathways in Mathematics
Inhalt: xi
316 S.
15 s/w Illustr.
1 farbige Illustr.
316 p. 16 illus.
1 illus. in color.
ISBN-13: 9783030772628
ISBN-10: 3030772624
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Bellaïche, Joël
Auflage: 1st ed. 2021
Hersteller: Springer International Publishing
Springer International Publishing AG
Pathways in Mathematics
Maße: 241 x 160 x 24 mm
Von/Mit: Joël Bellaïche
Erscheinungsdatum: 13.08.2021
Gewicht: 0,658 kg
Artikel-ID: 119926853
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