| Softcover ISBN: | 978-0-8218-1179-5 |
| Product Code: | CRMM/3.S |
| List Price: | $49.00 |
| MAA Member Price: | $44.10 |
| AMS Member Price: | $39.20 |
| eBook ISBN: | 978-1-4704-3849-4 |
| Product Code: | CRMM/3.E |
| List Price: | $45.00 |
| MAA Member Price: | $40.50 |
| AMS Member Price: | $36.00 |
| Softcover ISBN: | 978-0-8218-1179-5 |
| eBook: ISBN: | 978-1-4704-3849-4 |
| Product Code: | CRMM/3.S.B |
| List Price: | $94.00 $71.50 |
| MAA Member Price: | $84.60 $64.35 |
| AMS Member Price: | $75.20 $57.20 |
| Softcover ISBN: | 978-0-8218-1179-5 |
| Product Code: | CRMM/3.S |
| List Price: | $49.00 |
| MAA Member Price: | $44.10 |
| AMS Member Price: | $39.20 |
| eBook ISBN: | 978-1-4704-3849-4 |
| Product Code: | CRMM/3.E |
| List Price: | $45.00 |
| MAA Member Price: | $40.50 |
| AMS Member Price: | $36.00 |
| Softcover ISBN: | 978-0-8218-1179-5 |
| eBook ISBN: | 978-1-4704-3849-4 |
| Product Code: | CRMM/3.S.B |
| List Price: | $94.00 $71.50 |
| MAA Member Price: | $84.60 $64.35 |
| AMS Member Price: | $75.20 $57.20 |
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Book DetailsCRM Monograph SeriesVolume: 3; 1993; 112 ppMSC: Primary 14; Secondary 11
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
Titles in this series are co-published with the Centre de recherches mathématiques.
ReadershipGraduate students and researchers wishing an introduction to the subject.
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Table of Contents
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Chapters
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Introduction
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Chapter 1. Riemann surfaces
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Chapter 2. Riemann-Roch theorem
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Chapter 3. Abel-Jacobi theorem and period relations
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Chapter 4. Divisors and theta functions
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Chapter 5. Dimension of the space of theta functions
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Chapter 6. Projective embedding and theta functions
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Chapter 7. Elliptic curves as the intersection of two quadrics
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Chapter 8. The Fermat curve
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Chapter 9. Discrete subrgroups of SL(sub 2)(R)
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Chapter 10. Riemann surface structure of $\Gamma \setminus \mathcal H^*$
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Chapter 11. The modular curve X(N)
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Chapter 12. Generalities on abelian varieties
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Chapter 13. The conjecture of Tate
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Chapter 14. Finiteness of isogeny classes
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Chapter 15. Mordell’s conjecture
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Reviews
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Grew out of a one-semester course given by the author ... The notes of this course ... have gained a remarkable popularity among students and teachers, mainly for their efficient arrangement, enlightening style, self-containedness and—nevertheless manageable—conciseness. The book ... preserves the style of these lectures and, in this way, makes them available to a wider class of readers who wish an independent, brief introduction to the subject of abelian varieties.
Zentralblatt MATH
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Reviews
- Requests
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
Titles in this series are co-published with the Centre de recherches mathématiques.
Graduate students and researchers wishing an introduction to the subject.
-
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
-
Grew out of a one-semester course given by the author ... The notes of this course ... have gained a remarkable popularity among students and teachers, mainly for their efficient arrangement, enlightening style, self-containedness and—nevertheless manageable—conciseness. The book ... preserves the style of these lectures and, in this way, makes them available to a wider class of readers who wish an independent, brief introduction to the subject of abelian varieties.
Zentralblatt MATH
