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bellaïche joël - the eigenbook

The Eigenbook Eigenvarieties, families of Galois representations, p-adic L-functions

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Lingua: Inglese


Pubblicazione: 08/2022
Edizione: 1st ed. 2021


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.


- 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.


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.

Altre Informazioni



Condizione: Nuovo
Collana: Pathways in Mathematics
Dimensioni: 235 x 155 mm Ø 504 gr
Formato: Brossura
Illustration Notes:XI, 316 p. 16 illus., 1 illus. in color.
Pagine Arabe: 316
Pagine Romane: xi

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