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Small points on subvarieties of a torus
 Journal
, 2009
"... Abstract. Let V be a subvariety of a torus defined over the algebraic numbers. We give a qualitative and quantitative description of the set of points of V of height bounded by invariants associated to any variety containing V. Especially, we determine whether such a set is or not dense in V. We the ..."
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Abstract. Let V be a subvariety of a torus defined over the algebraic numbers. We give a qualitative and quantitative description of the set of points of V of height bounded by invariants associated to any variety containing V. Especially, we determine whether such a set is or not dense in V. We then prove that these sets can always be written as the intersection of V with a finite union of translates of tori of which we control the sum of the degrees. As a consequence, we prove a conjecture by the first author and David up to a logarithmic factor. 1.