Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2

Häftad, Engelska, 1996

Del 230 i serien London Mathematical Society Lecture Note Series

1 051 kr

Beställningsvara. Skickas inom 3-6 vardagar. Fri frakt över 249 kr.

Beskrivning

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.

Produktinformation

Utgivningsdatum:1996-04-18
Mått:152 x 228 x 16 mm
Vikt:342 g
Format:Häftad
Språk:Engelska
Serie:London Mathematical Society Lecture Note Series
Antal sidor:236
Förlag:Cambridge University Press
ISBN:9780521483704

Utforska kategorier

Talteori inom Naturvetenskap och teknik

Recensioner i media

'… this textbook provides an excellent treatment of the subject of the basic algebraic geometry (and arithmetic) of genus 2 curves and would serve as a useful introductory text for graduate students.' A Maciocia, Proceedings of the Edinburgh Mathematical Society

Innehållsförteckning

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.