7. Bounding l-torsion in class groups of families of number fields | Turnage Butterbaugh | 2017

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

Connections For Women: Analytic Number Theory February 02, 2017 - February 03, 2017

February 03, 2017 (10:45 AM PST - 11:45 AM PST)
Speaker(s): Caroline Turnage-Butterbaugh (Duke University)
Location: MSRI: Simons Auditorium

Abstract
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