The Cohen-Lenstra heuristics are influential conjectures in arithmetic statistics from 1984 which predict the average number of p-torsion elements in class groups of quadratic fields, for p an odd prime. So far, this average number has only been computed for p = 3. In joint work with Ishan Levy, we verify this prediction for arbitrary p over suitable function fields. The key input to the proof is a computation of the stable homology of Hurwitz spaces associated to dihedral groups.

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