How Many Rational Points Can a Curve Have?
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.
KeywordsRational Point Tangent Plane Number Field Rational Curf Hyperplane Section
Unable to display preview. Download preview PDF.
- ACGH] E.Arbarello, M.Cornalba, P.Griffiths, J.Harris. Geometry of Algebraic Curves, Volume 1. Springer-Verlag, NY.Google Scholar
- C]L.Caporaso. Distribution of rational points and Kodaira dimension of fiber products. This volume, 1-12.Google Scholar
- CHM] L.Caporaso, J.Harris, B.Mazur. Uniformity of rational points. To appear in JAMS.Google Scholar
- L]S.Lang. Hyperbolic and diophantine analysis. Bull. Amer. Math. Soc. 14, No. 2 (1986), 159–205.Google Scholar
- S]B.Segre. The maximum number of lines lying on a quartic surface. Quart. J. Math. (1943), 86–96.Google Scholar