Prolegomena to a middlebrow arithmetic of curves of genus 2
Author(s)
Bibliographic Information
Prolegomena to a middlebrow arithmetic of curves of genus 2
（London Mathematical Society lecture note series, 230）
Cambridge University Press, 1996
- : pbk
Available at 83 libraries
Note
Includes bibliography (p. [207]-218) and index rerum et personarum
Description and Table of Contents
Description
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. Included is an explicit treatment of the Jacobian, which throws new light onto the geometry of the Kummer surface. The Mordell-Weil group can then be determined for many curves, and in many non-trivial cases all rational points can be found. 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 into the arithmetic of curves of genus 2.
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.
by "Nielsen BookData"