Courbes algébriques et équations multiplicatives

  title={Courbes alg{\'e}briques et {\'e}quations multiplicatives},
  author={Guillaume Maurin},
  journal={Mathematische Annalen},
We study the intersection of an algebraic curve C lying in a multiplicative torus over $${\bar{\mathbb{Q}}}$$ with the union of all algebraic subgroups of codimension 2. Finiteness of this set has already been proved by Bombieri, Masser and Zannier under the assumption that C is not contained in a translate of a proper subtorus. Following this result, the question of the minimal hypothesis implying finiteness has been raised by these authors, giving rise to the conjecture~: finiteness holds… CONTINUE READING