Thursday, October 21
Milner 216, 1:00 PM
Title: Galois representations on fundamental groups
Abstract: Let l be a prime. There is a Galois representation on the outer automorphisms of the pro-l fundamental group of the projective line minus three points. The kernel of this representation defines an extension of Q. Although well-studied, the size of this extension is still unknown. However, the nature of this extension can be studied by way of a related question: Which curves with good reduction away from l admit unramified l-covers of X? The l-power torsion of such curves is rational over this extension. In this talk, I will explain this relation, and present some explicit results for the case of elliptic curves when l=2.