The Eigenbook: Eigenvarieties, families of Galois representations, p-adic L-functions: Pathways in Mathematics
Autor Joël Bellaïcheen Limba Engleză Hardback – 13 aug 2021
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.
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Specificații
ISBN-13: 9783030772628
ISBN-10: 3030772624
Pagini: 316
Ilustrații: XI, 316 p. 16 illus., 1 illus. in color.
Dimensiuni: 155 x 235 x 40 mm
Greutate: 0.64 kg
Ediția:1st ed. 2021
Editura: Springer International Publishing
Colecția Birkhäuser
Seria Pathways in Mathematics
Locul publicării:Cham, Switzerland
ISBN-10: 3030772624
Pagini: 316
Ilustrații: XI, 316 p. 16 illus., 1 illus. in color.
Dimensiuni: 155 x 235 x 40 mm
Greutate: 0.64 kg
Ediția:1st ed. 2021
Editura: Springer International Publishing
Colecția Birkhäuser
Seria Pathways in Mathematics
Locul publicării:Cham, Switzerland
Cuprins
- 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.
Recenzii
“This book represented hope. If I read it carefully, maybe I would finally get to know what they were all talking about, and gain some real insight into what are obviously very important and influential ideas. While I cannot claim to be an expert by now, my first skim through, skipping all the exercises, has provided me with a satisfying foundation, and I found that revisited passages responded well to a second reading to consolidate what I had learned.” (Neil P. Dummigan, Mathematical Reviews, May, 2023)
“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 Dąbrowski, zbMATH 1493.11002, 2022)
Notă biografică
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.
Textul de pe ultima copertă
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.
Written in an engaging and educational style, the book also includes exercises and provides their solution.
Caracteristici
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