Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes
/ Oratrice : Laura Capuano (Roma Tre, Italie)
Given n multiplicatively independent rational functions $f_1, \ldots, f_n$ with rational coefficients, there are at most finitely many complex numbers $a$ such that $f_1(a), \ldots, f_n(a)$ satisfy two independent multiplicative relations. This was proved independently by Maurin and Bombieri, Habegger, Masser and Zannier and is an instance of more general conjectures on unlikely intersections over tori. After a general introduction on these type of questions, in this talk we will address a positive characteristic variant of this problem proving some uniformity results about the cardinality of the sets involved. This is a joint work with F. Barroero, L. Mérai, A. Ostafe and M. Sha.