Abelian arboreal representations

Abstract: I will present joint work with Andrea Ferraguti which makes progress on a Conjecture of Andrews and Petsche that classifies abelian dynamical Galois groups over number fields, in the unicritical case. I will explain how to reduce the conjecture to the post-critically finite case and the key tools to handle all unicritical PCF with periodic critical orbit over any number field and all PCF over quadratic number fields. Along the way I will present an earlier rigidity result of ours on the maximal closed subgroup of the automorphism group of a binary rooted tree, which offered us with the main input to translate the commutativity of the Galois image into diophantine equations. I will also overview progress on the tightly related problem of lower bounding arboreal degrees.

algebraic geometrynumber theory

Audience: researchers in the topic

Comments: Zoom Meeting ID: 856 1386 0958 Passcode: 513992

FGC-HRI-IPM Number Theory Webinars

Series comments: password is 848084