Small points on subvarieties of a torus

Francesco Amoroso (1) , Evelina Viada (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 Department of Mathematics [Basel]

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.

Domaines: Théorie des nombres [math.NT]

Francesco Amoroso, Evelina Viada. Small points on subvarieties of a torus. Duke Mathematical Journal, 2009, 150 (3), pp.407-442. ⟨hal-00424769⟩