The Cohen--Lenstra moments over function fields via the stable homology of non-splitting Hurwitz spaces
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909817084313600 |
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| author | Landesman, Aaron Levy, Ishan |
| author_facet | Landesman, Aaron Levy, Ishan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Cohen--Lenstra moments over function fields via the stable homology of non-splitting Hurwitz spaces Landesman, Aaron Levy, Ishan Number Theory Algebraic Geometry Algebraic Topology 11R29, 11R11, 11R58, 55P43 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. |
| title | The Cohen--Lenstra moments over function fields via the stable homology of non-splitting Hurwitz spaces |
| topic | Number Theory Algebraic Geometry Algebraic Topology 11R29, 11R11, 11R58, 55P43 |
| url | https://arxiv.org/abs/2410.22210 |