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London Mathematical Society Lecture Note Ser.: Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2 by E. V. Flynn and J. W. S. Cassels (1996, Trade Paperback)
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About this product
Product Identifiers
PublisherCambridge University Press
ISBN-100521483700
ISBN-139780521483704
eBay Product ID (ePID)1035182
Product Key Features
Number of Pages236 Pages
LanguageEnglish
Publication NameProlegomena to a Middlebrow Arithmetic of Curves of Genus 2
SubjectNumber Theory, Geometry / Algebraic
Publication Year1996
TypeTextbook
Subject AreaMathematics
AuthorE. V. Flynn, J. W. S. Cassels
SeriesLondon Mathematical Society Lecture Note Ser.
FormatTrade Paperback
Dimensions
Item Height0.6 in
Item Weight12.1 Oz
Item Length9 in
Item Width6 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN96-011647
Dewey Edition20
Reviews'... 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, 'It is clear that this often subtle and witty book is required reading for those working in the field.'J. Schoissengeier, Wien, Monatshefte für Mathematik, '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, "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, '... 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, ‘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, 'It is clear that this often subtle and witty book is required reading for those working in the field.' J. Schoissengeier, Wien, , Monatshefte fr Mathematik, '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, 'It is clear that this often subtle and witty book is required reading for those working in the field.' J. Schoissengeier, Wien, , Monatshefte f r Mathematik, ‘It is clear that this often subtle and witty book is required reading for those working in the field.’J. Schoissengeier, Wien, Monatshefte für Mathematik, 'It is clear that this often subtle and witty book is required reading for those working in the field.' J. Schoissengeier, Wien, Monatshefte für Mathematik, ‘… the authors adopt a down-to-earth approach, assuming a fair background in algebraic geometry, but explaining carefully the tools used.’Mathematika, '... the authors adopt a down-to-earth approach, assuming a fair background in algebraic geometry, but explaining carefully the tools used.'Mathematika, '… the authors adopt a down-to-earth approach, assuming a fair background in algebraic geometry, but explaining carefully the tools used.' Mathematika, '… 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, '... 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, ‘… 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
Series Volume NumberSeries Number 230
IllustratedYes
Dewey Decimal516.3/52
Table Of ContentBackground 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.
SynopsisThe 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., 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. The work is accessible to beginning graduate students in number theory, algebraic geometry and workers in related areas.
LC Classification NumberQA565 .C38 1996
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