Uniformity of rational points over all quadratic fields

Details Uniformity of rational points over all quadratic fields Uniformity of rational points over all quadratic fields

1994-11-24

arxiv.org/abs/alg-geom/9411015v2

Mathematics

Algebraic Geometry

4 pages, LaTeX. "Final" version. Urges of doubters of people's sense of humor followed; jokes removed. Jokes available from au

Scientific paper

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 degr\'e $\leq 3$ de $K$ et $C$ est une courbe lisse projective
conn\`exe, de genre $g$ d\'efinie sur $L$ on a $$\# C(L) < N(K,g). $$

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