00:00:00 / 00:00:00

The average size of 3-torsion in class groups of 2-extensions

By Melanie Matchett Wood

Appears in collection : Jean-Morlet Chair - Conference - Arithmetic Statistics / Chaire Jean-Morlet - Conférence - Statistiques arithmétiques

We determine the average size of the 3-torsion in class groups of $G$-extensions of a number field when $G$ is any transitive 2 -group containing a transposition, for $\theta$-xample $D_4$. It follows from the Cohen--Lenstra--Martinet heuristics that the average size of the $p$-torsion in class groups of $G$-extensions of a number field is conjecturally finite for any $G$ and most $p$ (including $p \nmid|G|$ ). Previously this conjecture had only been proven in the cases of $G=S_2$ with $p=3$ and $G=S_3$ with $p=2$. We also show that the average 3-torsion in a certain relative class group for these $G$-extensions is as predicted by Cohen and Martinet, proving new cases of the Cohen--Lenstra--Martinet heuristics. Our new method also works for many other permutation groups $G$ that are not 2-groups.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.20046503
  • Cite this video Matchett Wood Melanie (5/15/23). The average size of 3-torsion in class groups of 2-extensions. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20046503
  • URL https://dx.doi.org/10.24350/CIRM.V.20046503



  • OLIVER, Robert J. Lemke, WANG, Jiuya, et WOOD, Melanie Matchett. The average size of $3 $-torsion in class groups of $2 $-extensions. arXiv preprint arXiv:2110.07712, 2021. - https://doi.org/10.48550/arXiv.2110.07712

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow


  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
  • Get notification updates
    for your favorite subjects
Give feedback