Homological stability for Hurwitz spaces and applications

Fuente: arXiv
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Autori principali: Landesman, Aaron, Levy, Ishan
Natura: Preprint
Pubblicazione: 2025
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author Landesman, Aaron
Levy, Ishan
author_facet Landesman, Aaron
Levy, Ishan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2503_03861
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Homological stability for Hurwitz spaces and applications
Landesman, Aaron
Levy, Ishan
Algebraic Topology
Algebraic Geometry
Number Theory
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.
title Homological stability for Hurwitz spaces and applications
topic Algebraic Topology
Algebraic Geometry
Number Theory
url https://arxiv.org/abs/2503.03861