Sur la conjecture abc, version corps de fonctions d'Oesterle

Details Sur la conjecture abc, version corps de fonctions d'Oesterle Sur la conjecture abc, version corps de fonctions d'Oesterle

2007-03-16

arxiv.org/abs/math/0703502v2

Mathematics

Number Theory

withdrawn.Conjecture already known by results of McQuillan and K. Yamanoi

Scientific paper

We show a weak form of the function field version of Oesterle's abc conjecture. It asserts that, if $B$ is a complex projective connected curve, the number of intersection points, counted without multiplicities, of a fixed divisor $D$ of degree $d>0$ over $B$ with the graph $H$ of a section $h:B\to B\times \bP^1$ to the first projection is at least $(d-2)n-C(B,D)$, where $n$ is the degree of $H$ over $\bP^1$, and $C(D,B)$ a constant depending only on these two data. We show this number is at least $(d-2[\sqrt {d}]).n-C(D,B)$. The constant is ineffective.

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