Geodesic
On the density of S-adic integers near some projective G-varieties
Youssef Lazar1
1Imam Mohammad ibn Saud Islamic University (IMSIU), College of Science, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 48 (2023) no. 1, pp. 187-204

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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 some examples of applications for systems involving quadratic and linear forms.  
DOI : 10.54330/afm.127001
Keywords: Algebraic groups, projective variety, Adelic geometry, strong Approximation, quadratic forms

Youssef Lazar  1

1 Imam Mohammad ibn Saud Islamic University (IMSIU), College of Science, Department of Mathematics and Statistics 
Youssef Lazar. On the density of S-adic integers near some projective G-varieties. Annales Fennici Mathematici, Tome 48 (2023) no. 1, pp. 187-204. doi: 10.54330/afm.127001
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