Prolegomena to a middlebrow arithmetic of curves of genus 2 /

Prolegomena to a middlebrow arithmetic of curves of genus 2 /

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Bibliographic Details
Author / Creator:	Cassels, J. W. S. (John William Scott)
Imprint:	Cambridge ; New York : Cambridge University Press, 1996.
Description:	1 online resource (xiv, 218 pages) : illustrations.
Language:	English
Series:	London Mathematical Society lecture note series ; 230 London Mathematical Society lecture note series ; 230.
Subject:	Curves, Algebraic. Curves, Algebraic. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11180920

Hidden Bibliographic Details
Other authors / contributors:	Flynn, E. V.
ISBN:	9781107362178 1107362172 0521483700 9780521483704 9780511526084
Notes:	Includes bibliographical references (pages 207-218) and index. Print version record.
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. 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.
Other form:	Print version: Cassels, J.W.S. (John William Scott). Prolegomena to a middlebrow arithmetic of curves of genus 2. Cambridge ; New York : Cambridge University Press, 1996 0521483700

Table of Contents:

Ch. 1. Curves of genus 2
Ch. 2. Construction of the jacobian
Ch. 3. The Kummer surface
Ch. 4. The dual of the Kummer
Ch. 5. Weddle's surface
Ch. 6. [actual symbol not reproducible]
Ch. 7. The jacobian over local fields. Formal groups
Ch. 8. Torsion
Ch. 9. The isogeny. Theory
Ch. 10. The isogeny. Applications
Ch. 11. Computing the Mordell-Weil group
Ch. 12. Heights
Ch. 13. Rational points. Chabauty's Theorem
Ch. 14. Reducible jacobians
Ch. 15. The endomorphism ring
Ch. 16. The desingularized Kummer
Ch. 17. A neoclassical approach
Ch. 18. Zukunftsmusik
Appendix I. MAPLE programs
Appendix II. Files available by anonymous ftp.