Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2
$78.99 (C)
Part of London Mathematical Society Lecture Note Series
- Authors:
- J. W. S. Cassels, University of Cambridge
- E. V. Flynn, University of Liverpool
- Date Published: May 1996
- availability: Available
- format: Paperback
- isbn: 9780521483704
$
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(C)
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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.
Read more- Cassels is THE top person on this subject. His previous books have done very well
- This book is unique
- The subject matter is getting hotter all the time
Reviews & endorsements
"The volume is a comprehensive introduction to the burgeoning theory of computations on genus 2 curves and jacobians, clearly written and chock full of first-rate mathematical insights; it will certainly be the primary reference source for anyone wishing to study the subject." Joseph H. Silverman, Mathematical Reviews
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×Product details
- Date Published: May 1996
- format: Paperback
- isbn: 9780521483704
- length: 236 pages
- dimensions: 228 x 152 x 16 mm
- weight: 0.342kg
- availability: Available
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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