Rational points on families of curves with genus at least 2

DOI10.1006/jnth.1997.2146zbMath0896.11025OpenAlexW1992638917MaRDI QIDQ1376257

Teresa de Diego

Publication date: 18 December 1997

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1997.2146

zbMATH Keywords

elliptic curvesrational pointsalgebraic curvetheta divisorprojective varietiesjacobiansFalting's theoremSzpiro's conjectureNeron-Tate heightarbitrary genus

Mathematics Subject Classification ID

Rational points (14G05) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)]

Related Items (9)

Theta height and Faltings height ⋮ Bornes sur le nombre de points rationnels des courbes : en quête d’uniformité ⋮ Lower bound of the Néron-Tate height on abelian surfaces ⋮ Uniformity in Mordell-Lang for curves ⋮ The number of rational points on a curve of genus at least two ⋮ Unnamed Item ⋮ An application of Mumford's gap principle. ⋮ A criterion for transversality of curves and an application to the rational points ⋮ Computation of Sets of Rational Points of Genus-3 Curves via the Dem'Janenko–Manin Method

Cites Work

• Sur des hauteurs alternatives. I. (On alternative heights. I)
• Diophantine approximation on abelian varieties
• Finiteness theorems for abelian varieties over number fields.
• The canonical height and integral points on elliptic curves
• Siegel's theorem in the compact case
• Diophantine approximations and diophantine equations
• Theory of heights. With an appendix by Jürg Kramer: An alternative foundation of the Néron-Tate height
• Algebraic independence criteria.
• ESTIMATES FOR THE CHARACTERISTIC FUNCTION OF A PRIME IDEAL
• ESTIMATES FOR THE ORDERS OF ZEROS OF FUNCTIONS OF A CERTAIN CLASS AND APPLICATIONS IN THE THEORY OF TRANSCENDENTAL NUMBERS
• A Uniform Bound for Rational Points on Twists of a Given Curve
• Heights of Projective Varieties and Positive Green Forms
• Heights and the specialization map for families of abelian varieties.
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