Geometric modular forms and elliptic curves
 Responsibility
 Haruzo Hida.
 Language
 English.
 Edition
 2nd ed.
 Imprint
 Singapore ; Hackensack, NJ : World Scientific, c2012.
 Physical description
 xiii, 454 p. ; 24 cm.
Access
Available online
 ebooks.worldscinet.com World Scientific
 ebrary
Math & Statistics Library
Stacks
Call number  Status 

QA567.2 .E44 H53 2012  Unknown 
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Creators/Contributors
 Author/Creator
 Hida, Haruzo.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 437446) and index.
 Contents

 An AlgebroGeometric Tool Box Elliptic Curves Geometric Modular Forms Jacobians and Galois Representations Modularity Problems.
 (source: Nielsen Book Data)
 Publisher's Summary
 This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura  Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of twodimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction. In this new second edition, a detailed description of Barsotti  Tate groups (including formal Lie groups) is added to Chapter 1. As an application, a downtoearth description of formal deformation theory of elliptic curves is incorporated at the end of Chapter 2 (in order to make the proof of regularity of the moduli of elliptic curve more conceptual), and in Chapter 4, though limited to ordinary cases, newly incorporated are Ribet's theorem of full image of modular padic Galois representation and its generalization to 'big' lambdaadic Galois representations under mild assumptions (a new result of the author). Though some of the striking developments described above is out of the scope of this introductory book, the author gives a taste of present day research in the area of Number Theory at the very end of the book (giving a good account of modularity theory of abelian Qvarieties and Qcurves).
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 ISBN
 9789814368643 (hardcover : alk. paper)
 9814368644 (hardcover : alk. paper)