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How Many Rational Points Can a Curve Have?

  • Lucia Caporaso
  • Joe Harris
  • Barry Mazur
Part of the Progress in Mathematics book series (PM, volume 129)

Abstract

This paper is concerned with two conjectures in number theory describing the behavior of the number of rational points on an algebraic curve defined over a number field, as that curve varies.

Keywords

Rational Point Tangent Plane Number Field Rational Curf Hyperplane Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. ACGH] E.Arbarello, M.Cornalba, P.Griffiths, J.Harris. Geometry of Algebraic Curves, Volume 1. Springer-Verlag, NY.Google Scholar
  2. C]L.Caporaso. Distribution of rational points and Kodaira dimension of fiber products. This volume, 1-12.Google Scholar
  3. CHM] L.Caporaso, J.Harris, B.Mazur. Uniformity of rational points. To appear in JAMS.Google Scholar
  4. L]S.Lang. Hyperbolic and diophantine analysis. Bull. Amer. Math. Soc. 14, No. 2 (1986), 159–205.Google Scholar
  5. S]B.Segre. The maximum number of lines lying on a quartic surface. Quart. J. Math. (1943), 86–96.Google Scholar

Copyright information

© Birkhäuser Boston 1995

Authors and Affiliations

  • Lucia Caporaso
    • 1
  • Joe Harris
    • 1
  • Barry Mazur
    • 1
  1. 1.Mathematics DepartmentHarvard UniversityCambridgeUSA

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