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arXiv · alg-geom/9411015

Uniformity of rational points over all quadratic fields

Dan Abramovich
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Abstract

We refine a result of L. Caporaso, J. Harris and B. Mazur, and prove: Supposons que la conjecture de Lang soit vraie. Soit $K$ un corps des nombres et $g>1$ un entier. Il existe un nombre $N(K,g)$ tel que si $L$ est une extension de degré $\leq 3$ de $K$ et $C$ est une courbe lisse projective connèxe, de genre $g$ définie sur $L$ on a $$\# C(L) < N(K,g). $$

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Dan Abramovich. 1994-12-10. Uniformity of rational points over all quadratic fields. https://arxiv.org/abs/alg-geom/9411015

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