The stable homology of Hurwitz modules and applications
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912623326396416 |
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| author | Landesman, Aaron Levy, Ishan |
| author_facet | Landesman, Aaron Levy, Ishan |
| contents | We show that the homology of modules for Hurwitz spaces stabilizes and compute its stable value. As one consequence, we compute the moments of Selmer groups in quadratic twist families of abelian varieties over suitably large function fields. As a second consequence, we deduce a version of Bhargava's conjecture, counting the number of $S_d$ degree $d$ extensions of $\mathbb F_q(t)$, for suitably large $q$. As a third consequence, we deduce that the homology of Hurwitz spaces associated to racks with a single component satisfy representation stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02068 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The stable homology of Hurwitz modules and applications Landesman, Aaron Levy, Ishan Number Theory Algebraic Geometry Algebraic Topology We show that the homology of modules for Hurwitz spaces stabilizes and compute its stable value. As one consequence, we compute the moments of Selmer groups in quadratic twist families of abelian varieties over suitably large function fields. As a second consequence, we deduce a version of Bhargava's conjecture, counting the number of $S_d$ degree $d$ extensions of $\mathbb F_q(t)$, for suitably large $q$. As a third consequence, we deduce that the homology of Hurwitz spaces associated to racks with a single component satisfy representation stability. |
| title | The stable homology of Hurwitz modules and applications |
| topic | Number Theory Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2510.02068 |