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A Chebotarev density theorem for families of fields, with applications to class groups

Recent developments in Analytic Number Theory May 01, 2017 - May 05, 2017

May 02, 2017 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Lillian Pierce (Duke University)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Class groups

  • number fields

  • p-torsion

  • Chebotarev density theorem

  • Artin conjectures

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

Abstract

This talk will present a new effective Chebotarev theorem that holds for all but a possible zero-density subfamily of certain families of number fields of fixed degree. For certain families, this work is unconditional, and in other cases it is conditional on the strong Artin conjecture and certain conjectures on counting number fields. As a result, we obtain nontrivial average upper bounds on p-torsion in the class groups of the families of fields.

Supplements
28393?type=thumb Pierce.Notes 1.01 MB application/pdf Download
Video/Audio Files

Pierce

H.264 Video 5-Pierce.mp4 497 MB video/mp4 rtsp://videos.msri.org/data/000/028/304/original/5-Pierce.mp4 Download
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