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

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

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