The Eigenbook
Eigenvarieties, families of Galois representations, p-adic L-functions
1st Edition
Published on 14. August 2022
Book
Paperback/Softback
XI, 316 pages
978-3-030-77265-9 (ISBN)
Description
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.
Reviews / Votes
"Complete proofs (or detailed references) of all statements are given and many exercises (with their solutions or hints) are included, hence the book may be addressed to graduate students working in this beautiful area of number theory and arithmetic algebraic geometry. This is a welcome addition to the literature in a field." (Andrzej Dabrowski, zbMATH 1493.11002, 2022)"Complete proofs (or detailed references) of all statements are given and many exercises (with their solutions or hints) are included, hence the book may be addressed to graduate students working in this beautiful area of number theory and arithmetic algebraic geometry. This is a welcome addition to the literature in a field." (Andrzej Dabrowski, zbMATH 1493.11002, 2022)
More details
Product info
Paperback
Series
Edition
1st ed. 2021
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
15
1 farbige Abbildung, 15 s/w Abbildungen
XI, 316 p. 16 illus., 1 illus. in color.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 18 mm
Weight
499 gr
ISBN-13
978-3-030-77265-9 (9783030772659)
DOI
10.1007/978-3-030-77263-5
Schweitzer Classification
Other editions
Additional editions
Book
08/2021
1st Edition
Birkhäuser
€69.54
Shipment within 7-9 days
Person
Joel Bellaiche studied at the Ecole Normale Superieure 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.
<b>Joel Bellaiche</b> studied at the Ecole Normale Superieure 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.
<b>Joel Bellaiche</b> studied at the Ecole Normale Superieure 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.
Content
- Introduction.- <b>Part I The 'Eigen' Construction</b>.- Eigenalgebras.- Eigenvarieties.- <b>Part II Modular Symbols and <i>L</i>-Functions</b>.- Abstract Modular Symbols.- Classical Modular Symbols, Modular Forms, <i>L</i>-functions.- Rigid Analytic Modular Symbols and <i>p</i>-Adic <i>L</i>-functions.- <b>Part III The Eigencurve and its <i>p</i>-Adic <i>L</i>-Functions</b>.- The Eigencurve of Modular Symbols.- <i>p</i>-Adic <i>L</i>-Functions on the Eigencurve.- The Adjoint <i>p</i>-Adic <i>L</i>-Function and the Ramification Locus of the Eigencurve.- Solutions and Hints to Exercises.