Seminario: "Arboreal Galois representations and a geometric surjectivity theorem" - Andrea Ferraguti
Joint seminar di Teoria dei Numeri dell'Università e del Politecnico di Torino.
"Arboreal Galois representations and a geometric surjectivity theorem"
Andrea Ferraguti - Instituto de Ciencias Matematicas, Madrid
Giovedì 13 Febbraio 2020 - ore 16:00
Aula Buzano - Dipartimento di Scienze Matematiche
Politecnico di Torino
Abstract: Arboreal Galois representations are central objects in modern arithmetic dynamics. They are built from the iterations of a rational map of the projective line, and they encode in a beatiful way arithmetic, combinatorial and group-theoretic information about the absolute Galois group of a field. In this talk, we will recall the construction, the basic properties and some peculiar examples. Afterwards, we will explain the ideas behind our recent proof of Jones' conjecture, that allows to construct infinite families of geometrically surjective arboreal representations in any characteristic. The key ingredient is a new effective, uniform bound for the height of integral points on elliptic curves over global function fields. This is joint work with G. Micheli.