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arXiv · 2503.03861

Homological stability for Hurwitz spaces and applications

Aaron Landesman·Ishan Levy
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Abstract

We show the homology of the Hurwitz space associated to an arbitrary finite rack stabilizes integrally in a suitable sense. We also compute the dominant part of its stable homology after inverting finitely many primes. This proves a conjecture of Ellenberg--Venkatesh--Westerland and improves upon our previous results for non-splitting racks. We obtain applications to Malle's conjecture, the Picard rank conjecture, and the Cohen--Lenstra--Martinet heuristics.

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Aaron Landesman, Ishan Levy. 2025-03-05. Homological stability for Hurwitz spaces and applications. https://arxiv.org/abs/2503.03861

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