Abelian varieties with maximal Galois action on their torsion points

Joint IAS/PU Number Theory Seminar
Topic:Abelian varieties with maximal Galois action on their torsion points
Speaker:David Zywina
Affiliation:Queen's University; Member, School of Mathematics
Date:Thursday, January 24
Time/Room:4:30pm - 5:30pm/S-101
Video Link:https://video.ias.edu/1213/jointiaspu/0124-DavidZywina

Abstract: Associated to an abelian variety A/K is a Galois representation which describes the action of the absolute Galois group of K on the torsion points of A. In this talk, we shall describe how large the image of this representation can be (in terms of a number field K and the dimension of A). We achieve this by considering abelian varieties in families and then using a special variant of Hilbert's irreducibility theorem. Some results of Serre on the mod ell Galois image will also be reviewed. (This is joint work with David Zureick-Brown)