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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
Tags/Keywords
  • number fields

  • l-torsion

  • Class groups

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Bounding L-Torsion In Class Groups Of Families Of Number Fields Of Arbitrary Degree

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

Supplements
27893?type=thumb Butterbaugh Notes 255 KB application/pdf Download
Video/Audio Files

Bounding L-Torsion In Class Groups Of Families Of Number Fields Of Arbitrary Degree

H.264 Video 07-Turnage-Butterbaugh.mp4 135 MB video/mp4 rtsp://videos.msri.org/data/000/027/808/original/07-Turnage-Butterbaugh.mp4 Download
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