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• W2938700811 abstract "Consider a one-parameter family of smooth, irreducible, projective curves of genus $gge 2$ defined over a number field. Each fiber contains at most finitely many rational points by the Mordell Conjecture, a theorem of Faltings. We show that the number of rational points is bounded only in terms of the family and the Mordell--Weil rank of the fiber's Jacobian. Our proof uses Vojta's approach to the Mordell Conjecture furnished with a height inequality due to the second- and third-named authors. In addition we obtain uniform bounds for the number of torsion in the Jacobian that lie each fiber of the family." @default.
• W2938700811 created "2019-04-25" @default.
• W2938700811 creator A5048527494 @default.
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• W2938700811 date "2019-04-15" @default.
• W2938700811 modified "2023-09-25" @default.
• W2938700811 title "Uniform bound for the number of rational points on a pencil of curves" @default.
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