The Eigenbook Eigenvarieties families of Galois representations p adic L functions 1st Edition Joël Bellaïche 9783030772635 3030772632

The Eigenbook Eigenvarieties families of Galois representations p adic L functions 1st Edition Joël Bellaïche – Ebook Instant Download/Delivery ISBN(s): 9783030772628, 9783030772635, 3030772624, 3030772632

Product details:

• ISBN 10: 3030772632
• ISBN 13: 9783030772635
• Author:  Joël Bellaïche 

​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.

Table contents:

1. Introduction
Part I. The ‘Eigen’ Construction
2. Eigenalgebras
3. Eigenvarieties
Part II. Modular Symbols and L-Functions
4. Abstract Modular Symbols
5. Classical Modular Symbols, Modular Forms, L-functions
6. Rigid Analytic Modular Symbols and p-Adic L-functions
Part III. The Eigencurve and its p-Adic L-Functions
7. The Eigencurve of Modular Symbols
8. p-Adic L-Functions on the Eigencurve
9. The Adjoint p-Adic L-Function and the Ramification Locus of the Eigencurve
10. Solutions and Hints to Exercises

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