Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2
The number theoretic properties of curves of genus 2 are attracting increasing attention. This book provides new insights into this subject; much of the material here is entirely new, and none has appeared in book form before. The authors include an explicit treatment of the Jacobian, which throws new light onto the geometry of the Kummer surface. Mathematicians can then determine the Mordell-Weil group for many curves, and in many nontrivial cases they can find all rational points. The results exemplify the power of computer algebra in diophantine contexts, but computer expertise is not assumed in the main text. Number theorists, algebraic geometers and workers in related areas will find that this book offers unique insights.
1100958505
Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2
The number theoretic properties of curves of genus 2 are attracting increasing attention. This book provides new insights into this subject; much of the material here is entirely new, and none has appeared in book form before. The authors include an explicit treatment of the Jacobian, which throws new light onto the geometry of the Kummer surface. Mathematicians can then determine the Mordell-Weil group for many curves, and in many nontrivial cases they can find all rational points. The results exemplify the power of computer algebra in diophantine contexts, but computer expertise is not assumed in the main text. Number theorists, algebraic geometers and workers in related areas will find that this book offers unique insights.
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Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2

Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2

by J. W. S. Cassels, E. V. Flynn
Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2

Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2

by J. W. S. Cassels, E. V. Flynn

Overview

The number theoretic properties of curves of genus 2 are attracting increasing attention. This book provides new insights into this subject; much of the material here is entirely new, and none has appeared in book form before. The authors include an explicit treatment of the Jacobian, which throws new light onto the geometry of the Kummer surface. Mathematicians can then determine the Mordell-Weil group for many curves, and in many nontrivial cases they can find all rational points. The results exemplify the power of computer algebra in diophantine contexts, but computer expertise is not assumed in the main text. Number theorists, algebraic geometers and workers in related areas will find that this book offers unique insights.

Product Details

ISBN-13: 9780521483704
Publisher: Cambridge University Press
Publication date: 04/18/1996
Series: London Mathematical Society Lecture Note Series , #230
Pages: 236
Product dimensions: 5.98(w) x 8.98(h) x 0.63(d)

Table of Contents

Background and conventions; 1. Curves of genus 2; 2. Construction of the jacobian; 3. The Kummer surface; 4. The dual of the Kummer; 5. Weddle's surface; 6. G/2G; 7. The jacobian over local fields; Formal groups; 8. Torsion; 9. The isogeny; Theory; 10. The isogeny; Applications; 11. Computing the Mordell-Weil group; 12. Heights; 13. Rational points Chabauty's theorem; 14. Reducible jacobians; 15. The endomorphism ring; 16. The desingularized Kummer; 17. A neoclassical approach; 18. Zukunftsmusik; Appendix 1. MAPLE programs; Appendix 2. Files available by FTP.
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