Moduli Theory and Arithmetic of Algebraic Varieties
نویسنده
چکیده
This paper surveys a few applications of algebro-geometric moduli theory to issues concerning the distribution of rational points in algebraic varieties. A few well known arithmetic problems with their expected answers (the socalled “diophantine conjectures”) are introduced in section 2, explaining their connection with a circle of ideas, whose goal is to find a unifying theme in analytic, differential, algebraic and arithmetic geometry. In section 3 we illustrate how, applying the modern moduli theory of algebraic varieties, the diophantine conjectures imply uniform boundedness of rational points on curves, which is also open. The crucial tool is an algebro-geometric
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