Duke Mathematical Journal
- Duke Math. J.
- Volume 168, Number 3 (2019), 377-427.
Nonabelian Cohen–Lenstra moments
In this article, we give a conjecture for the average number of unramified -extensions of a quadratic field for any finite group . The Cohen–Lenstra heuristics are the specialization of our conjecture to the case in which is abelian of odd order. We prove a theorem toward the function field analogue of our conjecture and give additional motivations for the conjecture, including the construction of a lifting invariant for the unramified -extensions that takes the same number of values as the predicted average and an argument using the Malle–Bhargava principle. We note that, for even , corrections for the roots of unity in are required, which cannot be seen when is abelian.
Duke Math. J., Volume 168, Number 3 (2019), 377-427.
Received: 22 February 2017
Revised: 6 July 2018
First available in Project Euclid: 29 January 2019
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Wood, Melanie Matchett. Nonabelian Cohen–Lenstra moments. Duke Math. J. 168 (2019), no. 3, 377--427. doi:10.1215/00127094-2018-0037. https://projecteuclid.org/euclid.dmj/1548730815