On the density of S-adic integers near some projective G-varieties
Keywords:Algebraic groups, projective variety, Adelic geometry, strong Approximation, quadratic forms
AbstractWe 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.
How to Cite
Lazar, Y. (2023). On the density of S-adic integers near some projective G-varieties. Annales Fennici Mathematici, 48(1), 187–204. https://doi.org/10.54330/afm.127001
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