Number Theory Seminar

Thursday 10/13/05 4:00-5:00 PM in Hylan 1106B:
Tom Tucker-"Shafarevich-Faltings theorems for rational maps"

ABSTRACT:

I will define a notion of "critical good reduction" for rational maps that has much in common with the usual notion of good reduction from algebraic geometry. We will then show that there are finitely many equivalence classes of rational maps with critically good reduction outside of a finite set of primes. The tools are Galois theory of number fields and function fields along with Siegel's theorem for integral points.