Abstract
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.
Citation
Melanie Matchett Wood. "Nonabelian Cohen–Lenstra moments." Duke Math. J. 168 (3) 377 - 427, 15 February 2019. https://doi.org/10.1215/00127094-2018-0037
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