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arXiv · 2410.22210

The Cohen--Lenstra moments over function fields via the stable homology of non-splitting Hurwitz spaces

Aaron Landesman·Ishan Levy
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Abstract

We compute the average number of surjections from class groups of quadratic function fields over $\mathbb F_q(t)$ onto finite odd order groups $H$, once $q$ is sufficiently large. These yield the first known moments of these class groups, as predicted by the Cohen--Lenstra heuristics, apart from the case $H = \mathbb Z/3\mathbb Z$. The key input to this result is a topological one, where we compute the stable rational homology groups of Hurwitz spaces associated to non-splitting conjugacy classes.

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BibTeXRIS

Aaron Landesman, Ishan Levy. 2024-10-29. The Cohen--Lenstra moments over function fields via the stable homology of non-splitting Hurwitz spaces. https://arxiv.org/abs/2410.22210

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