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Rational points on finite covers of \({\mathbb P}^{1}\) and \({\mathbb P}^{2}\). (English) Zbl 1054.14024

Summary: Let \(f:X\to \mathbb{P}^2_\mathbb{Q}\) be a finite cover of degree at least three, where \(X\) is integral. The author shows that the number of points of \(f(X(\mathbb{Q}))\) of multiplicative height at most \(B\) is \(O_{f,\varepsilon} (B^{2+ \varepsilon})\) for every \(\varepsilon >0\).

MSC:

14G05 Rational points
14H30 Coverings of curves, fundamental group
14E20 Coverings in algebraic geometry
11G35 Varieties over global fields
11G50 Heights
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References:

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