My Account
Log in Registration
All
Cart
Highlights
Fiction Books
Non-Fiction Books
Children's Books
Rare Books
Music
DVD & Blu-Ray
Video Games
Category
Wishlists
Cart
All
Free Shipping in the UK
Trustpilot
Proud to be B-Corp

Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2 J. W. S. Cassels (University of Cambridge)

Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2 By J. W. S. Cassels (University of Cambridge)

Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2 by J. W. S. Cassels (University of Cambridge)

Reviews:
£56.49
Condition - New
Only 2 left
New

Summary

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.

Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2 Summary

Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2 by J. W. S. Cassels (University of Cambridge)

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.

Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2 Reviews

'... 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
'... an explicit treatment.' L'Enseignement Mathematique
'It is clear that this often subtle and witty book is required reading for those working in the field.' J. Schoissengeier, Monatshefte fur Mathematik
'... the authors adopt a down-to-earth approach, assuming a fair background in algebraic geometry, but explaining carefully the tools used.' Mathematika
'The book is accessible without too many prerequisutes ... As a readable introduction to an exciting area of research in which there are may interesting questions still to be answered, the book is to be strongly recommended.' Bulletin of the London Mathematics Society

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.

Additional information

NLS9780521483704
9780521483704
0521483700
Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2 by J. W. S. Cassels (University of Cambridge)
J. W. S. Cassels (University of Cambridge)
London Mathematical Society Lecture Note Series
New
Paperback
Cambridge University Press
1996-04-18
236
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a new book - be the first to read this copy. With untouched pages and a perfect binding, your brand new copy is ready to be opened for the first time

Customer Reviews - Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2