The Vojta’s conjecture establishes geometrical conditions on the degeneracy of the set of S-integral points for an algebraic variety. The goal of the thesis is to prove that for certain algebraic varieties for which such conditions are not verified the set of S-integral points is Zariski-dense. Some effective methods in this respect has been developed by Beukers in his paper “Ternary form Equations” , in which he proved the density of integral solutions of some homogeneous diophantine equations. Following such ideas, the work of the thesis consists on finding the density of S-integral points on some varieties for which it is not known at the moment, imposing the needed arithmetical and geometrical conditions
Finding integral points on algebraic varieties
Di Tullio, Daniele
2017/2018
Abstract
The Vojta’s conjecture establishes geometrical conditions on the degeneracy of the set of S-integral points for an algebraic variety. The goal of the thesis is to prove that for certain algebraic varieties for which such conditions are not verified the set of S-integral points is Zariski-dense. Some effective methods in this respect has been developed by Beukers in his paper “Ternary form Equations” , in which he proved the density of integral solutions of some homogeneous diophantine equations. Following such ideas, the work of the thesis consists on finding the density of S-integral points on some varieties for which it is not known at the moment, imposing the needed arithmetical and geometrical conditionsFile | Dimensione | Formato | |
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https://hdl.handle.net/20.500.12608/28203