Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2
Seiten
1996
Cambridge University Press (Verlag)
978-0-521-48370-4 (ISBN)
Cambridge University Press (Verlag)
978-0-521-48370-4 (ISBN)
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 work is accessible to beginning graduate students in number theory, algebraic geometry and workers in related areas.
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.
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.
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.
| Erscheint lt. Verlag | 18.4.1996 |
|---|---|
| Reihe/Serie | London Mathematical Society Lecture Note Series |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 152 x 228 mm |
| Gewicht | 342 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| ISBN-10 | 0-521-48370-0 / 0521483700 |
| ISBN-13 | 978-0-521-48370-4 / 9780521483704 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Sieben ausgewählte Themenstellungen
Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
CHF 89,95
unlock your imagination with the narrative of numbers
Buch | Softcover (2024)
Advantage Media Group (Verlag)
CHF 27,90
Seltsame Mathematik - Enigmatische Zahlen - Zahlenzauber
Buch | Softcover (2024)
BoD – Books on Demand (Verlag)
CHF 27,95
