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

2019/04/24 by Youssef Lazar, Lazar, Youssef
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1904.10609

20 pages

arxiv created 2019/04/24 · arxiv updated 2019/04/25

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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