Joint IAS/Princeton University Number Theory Seminar

Let x_1, x_2,... be a sequence of n-tuples of roots of unity and suppose X is a subvariety of the algebraic torus. For a prime number p , Tate and Voloch proved that if the p-adic distance between x_k and X tends to 0 then all but finitely many sequence members lie on X . Buium and Scanlon later generalized this result. The distribution of those x_k that lie on X is governed by the classical (and resolved) Manin-Mumford Conjecture. I will present a modular variant of Tate and Voloch's discreteness result. It was motivated by the analogy between the conjectures of Manin-Mumford and Andre-Oort