# Bounding l-torsion in class groups of families of number fields of arbitrary degree

## Caroline Turnage-Butterbaugh (Duke)

Let K denote a number field of degree n, and for a fixed, positive integer l, consider the l-torsion subgroup of the class group of K. It is conjectured that the size of the this l-torsion subgroup is very small (in an appropriate sense), relative to the absolute discriminant of the field K. In 2007, Ellenberg and Venkatesh proved a nontrivial bound (removing a power from the trivial bound) by assuming GRH. In this talk, we will discuss a method that recovers this bound for almost all members of certain families of fields, without assuming GRH. This is joint work with Lillian Pierce and Melanie Matchett Wood.

Tuesday, April 11th, at 4:00pm in HBH 227