Skip to main content Accessibility help
×
  1. Home
  2. Books
  3. Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2
  • Cited by 124
      • Show more authors
      • You may already have access via personal or institutional login
    • Select format
    • Publisher:
      Cambridge University Press
      Publication date:
      November 2010
      April 1996
      ISBN:
      9780511526084
      9780521483704
      DOI:
      https://doi.org/10.1017/CBO9780511526084
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.342kg, 236 Pages
      • Subjects:
      Mathematics (general), Mathematics, Number Theory, Geometry and Topology
      Series:
      London Mathematical Society Lecture Note Series (230)
    You may already have access via personal or institutional login
    • Selected: Digital
    Add to cart View cart Buy from Cambridge.org
    Subjects:
    Mathematics (general), Mathematics, Number Theory, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (230)
    Information

    Book description

    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.

    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 Source: Proceedings of the Edinburgh Mathematical Society

    ‘… an explicit treatment.’

    Source: L'Enseignement Mathématique

    ‘It is clear that this often subtle and witty book is required reading for those working in the field.’

    J. Schoissengeier Source: Monatshefte für Mathematik

    ‘… the authors adopt a down-to-earth approach, assuming a fair background in algebraic geometry, but explaining carefully the tools used.’

    Source: 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.’

    Source: Bulletin of the London Mathematics Society

    Refine List

    Actions for selected content:

    Select all | Deselect all
    • View selected items
    • Export citations
    • Download PDF (zip)
    • Save to Kindle
    • Save to Dropbox
    • Save to Google Drive

    Save Search

    You can save your searches here and later view and run them again in "My saved searches".

    Please provide a title, maximum of 40 characters.
    Cancel
    ×

    Contents

    Contents

    Metrics

    Altmetric attention score

    Full text views

    Total number of HTML views: 0
    Total number of PDF views: 0 *
    Loading metrics...

    Book summary page views

    Total views: 0 *
    Loading metrics...

    * Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

    Usage data cannot currently be displayed.

    Accessibility standard: Unknown

    Why this information is here

    This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

    Accessibility Information

    Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.