Nonarchimedean Approximations by Special Points
Nonarchimedean Approximations by Special Points

Philipp Habegger , IAS
Fine Hall 214
Let x_1,x_2,... be a sequence of ntuples 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 padic 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) ManinMumford Conjecture. I will present a modular variant of Tate and Voloch's discreteness result. It was motivated by the analogy between the conjectures of ManinMumford and AndreOort.