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Introduction to Abelian Varieties

About this Title

V. Kumar Murty, University of Toronto, Toronto, ON, Canada

Publication: CRM Monograph Series
Publication Year: 1993; Volume 3
ISBNs: 978-0-8218-1179-5 (print); 978-1-4704-3849-4 (online)
DOI: https://doi.org/10.1090/crmm/003
MathSciNet review: MR1231797
MSC: Primary 14Kxx; Secondary 11G10, 14-00, 14K05

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Table of Contents

Front/Back Matter

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Chapters

• Introduction
• Chapter 1. Riemann surfaces
• Chapter 2. Riemann-Roch theorem
• Chapter 3. Abel-Jacobi theorem and period relations
• Chapter 4. Divisors and theta functions
• Chapter 5. Dimension of the space of theta functions
• Chapter 6. Projective embedding and theta functions
• Chapter 7. Elliptic curves as the intersection of two quadrics
• Chapter 8. The Fermat curve
• Chapter 9. Discrete subrgroups of SL(sub 2)(R)
• Chapter 10. Riemann surface structure of $\Gamma \setminus \mathcal H^*$
• Chapter 11. The modular curve X(N)
• Chapter 12. Generalities on abelian varieties
• Chapter 13. The conjecture of Tate
• Chapter 14. Finiteness of isogeny classes
• Chapter 15. Mordell’s conjecture

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