Rational points on Grassmannians and unlikely intersections in tori

Abstract

In this paper, we present an alternative proof of a finiteness theorem due to Bombieri, Masser and Zannier concerning intersections of a curve in the multiplicative group of dimension n with algebraic subgroups of dimension n-2. The proof uses a method introduced for the first time by Pila and Zannier to give an alternative proof of Manin-Mumford conjecture and a theorem to count points that satisfy a certain number of linear conditions with rational coefficients. This method has been largely used in many different problems in the context of "unlikely intersections".

16 pages

Cited by in corpus (3)

• Applications of the hyperbolic Ax-Schanuel conjecture
• Linear relations in families of powers of elliptic curves
• Unlikely Intersections in families of abelian varieties and the polynomial Pell equation