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Averages of p-torsion in class groups over function fields---good and bad primes

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

May 01, 2017 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Melanie Wood (University of California, Berkeley)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Class Field Theory

  • Cohen-Lenstra statistics

  • function fields

  • p-torsion

  • quadratic fields

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

Wood

Abstract

When we consider the average size of the p-torsion in class groups of quadratic fields, the behavior for p=2 is controlled by genus theory and is different from the conjectured behavior for odd primes, which is uniform in a certain sense over all odd primes. In this talk, we will consider the question when quadratic fields are replaced by fields of higher degree--for which primes p are the class group averages "bad" versus "good"? We will explain some theorems on class group averages for extensions of function fields that show some subtleties in the classification of good and bad primes

Supplements
28392?type=thumb Wood.Notes 616 KB application/pdf Download
Video/Audio Files

Wood

H.264 Video 4-Wood.mp4 377 MB video/mp4 rtsp://videos.msri.org/data/000/028/301/original/4-Wood.mp4 Download
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