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How Many Rational Points Can a Curve Have?

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The Moduli Space of Curves

Part of the book series: Progress in Mathematics ((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.

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References

  • ACGH] E.Arbarello, M.Cornalba, P.Griffiths, J.Harris. Geometry of Algebraic Curves, Volume 1. Springer-Verlag, NY.

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  • C]L.Caporaso. Distribution of rational points and Kodaira dimension of fiber products. This volume, 1-12.

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  • CHM] L.Caporaso, J.Harris, B.Mazur. Uniformity of rational points. To appear in JAMS.

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  • L]S.Lang. Hyperbolic and diophantine analysis. Bull. Amer. Math. Soc. 14, No. 2 (1986), 159–205.

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  • S]B.Segre. The maximum number of lines lying on a quartic surface. Quart. J. Math. (1943), 86–96.

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Author information

Authors and Affiliations

  1. Mathematics Department, Harvard University, 1 Oxford St., Cambridge, MA, 02138, USA

    Lucia Caporaso, Joe Harris & Barry Mazur

Authors
  1. Lucia Caporaso
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  2. Joe Harris
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  3. Barry Mazur
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Editor information

Editors and Affiliations

  1. Faculteit Wiskunde en Informatica, Universiteit van Amsterdam, 1018 TV, Amsterdam, The Netherlands

    Robbert H. Dijkgraaf , Carel F. Faber  & Gerard B. M. van der Geer ,  & 

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© 1995 Birkhäuser Boston

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Cite this paper

Caporaso, L., Harris, J., Mazur, B. (1995). How Many Rational Points Can a Curve Have?. In: Dijkgraaf, R.H., Faber, C.F., van der Geer, G.B.M. (eds) The Moduli Space of Curves. Progress in Mathematics, vol 129. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4264-2_2

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  • DOI: https://doi.org/10.1007/978-1-4612-4264-2_2

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8714-8

  • Online ISBN: 978-1-4612-4264-2

  • eBook Packages: Springer Book Archive

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