Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2

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August 2005



A unique insight into the topic of curves of genus 2, by two of the world's leading practitioners.


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.


'... 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, Wien, , 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
EAN: 9780521483704
ISBN: 0521483700
Untertitel: 'Cambridge Studies in Religious'. Sprache: Englisch.
Erscheinungsdatum: August 2005
Seitenanzahl: 236 Seiten
Format: kartoniert
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