# 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…

## Figures from this paper

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We compute all the moments of a normalization of the function that counts unramified $H_{8}$-extensions of quadratic fields, where $H_{8}$ is the quaternion group of order $8$, and show that the…

### Moments of unramified 2-group extensions of quadratic fields

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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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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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