Introduction to Abelian Varieties

Introduction to Abelian Varieties

by V. Kumar Murty
     
 

ISBN-10: 0821811797

ISBN-13: 9780821811795

Pub. Date: 03/01/2000

Publisher: American Mathematical Society

The book represents an introduction to the theory of abelian varieties with a view to arithmetic. The aim is to introduce some of the basics of the theory as well as some recent arithmetic applications to graduate students and researchers in other fields. The first part contains proofs of the Abel-Jacobi theorem, Riemann's relations and the Lefschetz theorem on

Overview

The book represents an introduction to the theory of abelian varieties with a view to arithmetic. The aim is to introduce some of the basics of the theory as well as some recent arithmetic applications to graduate students and researchers in other fields. The first part contains proofs of the Abel-Jacobi theorem, Riemann's relations and the Lefschetz theorem on projective embeddings over the complex numbers in the spirit of S. Lang's book Introduction to algebraic and abelian functions. Then the Jacobians of Fermat curves as well as some modular curves are discussed. Finally, as an application, Faltings' proof of the Mordell conjecture and its intermediate steps, the Tate conjecture and the Shafarevich conjecture, are sketched. — H. Lange for MathSciNet

Product Details

ISBN-13:
9780821811795
Publisher:
American Mathematical Society
Publication date:
03/01/2000
Series:
CRM Monograph Series, #3
Pages:
112
Product dimensions:
6.70(w) x 9.90(h) x 0.30(d)

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