The Eigenbook : Eigenvarieties, families of Galois representations, p-adic L-functions / Joël Bellaïche.

Format:

Book

Author/Creator:

Bellaïche, Joël, author.

Series:

Pathways in Mathematics, 2367-346X

Pathways in mathematics, 2367-3451

Language:

English

Subjects (All):

Number theory.

Physical Description:

1 online resource (XI, 316 p. 16 illus., 1 illus. in color.)

Edition:

1st ed. 2021.

Place of Publication:

Cham, Switzerland : Birkhäuser, [2021]

Summary:

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.

Contents:

- 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.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

3-030-77263-2

OCLC:

1263868884