Nonabelian Cohen–Lenstra moments

@article{Wood2019NonabelianCM,
  title={Nonabelian Cohen–Lenstra moments},
  author={Melanie Matchett Wood and Philip Matchett Wood},
  journal={Duke Mathematical Journal},
  year={2019}
}
In this paper we give a conjecture for the average number of unramified $G$-extensions of a quadratic field for any finite group $G$. The Cohen-Lenstra heuristics are the specialization of our conjecture to the case that $G$ is abelian of odd order. We prove a theorem towards the function field analog of our conjecture, and give additional motivations for the conjecture including the construction of a lifting invariant for the unramified $G$-extensions that takes the same number of values as… 

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We formulate a conjecture about moments of unramified extensions $L/K$ with $\left[K:\mathbb{Q}\right]=2$, $G\left(L/K\right)=H$ and $G\left(L/\mathbb{Q}\right)=G$ for any 2-group $G$. We prove a

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Cohen-Lenstra heuristics and local conditions

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  • 2018
We prove function field theorems supporting the Cohen–Lenstra heuristics for real quadratic fields, and natural strengthenings of these analogs from the affine class group to the Picard group of the

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