On the density of S-adic integers near some projective G-varieties

Youssef Lazar

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arXiv · 1904.10609

On the density of S-adic integers near some projective G-varieties

Youssef Lazar

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Abstract

We provide some general conditions which ensure that a system of inequalities involving homogeneous polynomials with coefficients in a S-adic field has nontrivial S-integral solutions. The proofs are based on the strong approximation property for Zariski-dense subgroups and adelic geometry of numbers. We give two examples of applications for systems involving quadratic and linear forms.

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Youssef Lazar. 2019-04-24. On the density of S-adic integers near some projective G-varieties. https://arxiv.org/abs/1904.10609

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