Algebra/Number Theory Seminar

Towards a finite index conjecture for iterated Galois groups

Tom Tucker, University of Rochester

Wednesday, March 8th, 2017
11:30 AM - 12:30 PM
Hylan 1106A

Let f be a polynomial over a global field. Let G denote the inverse limits of the Galois groups of f^n, where f^n denotes n-th iterate of f. Boston and Jones have suggested that under reasonable hypotheses, one might hope that G has finite index in the full group of automorphisms on an infinite tree corresponding to roots of iterates f^n when f is quadratic. We will show that their conjecture is true over function fields of characteristic 0, and that it would be a consequence of well-known diophantine conjectures over number fields. We will also treat the case of cubic polynomials, where less is known.

Event contact: dinesh dot thakur at rochester dot edu