Homological stability for Hurwitz spaces and applications
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866914068783169536 |
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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 |