The leading constant in Malle's conjecture over function fields
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908748181667840 |
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| author | Santens, Tim |
| author_facet | Santens, Tim |
| contents | We prove the analogue of Malle's conjecture for the global function field $\F_q(t)$ with $q$ sufficiently large, including a precise formula for the leading constant. The main ingredients are the recent breakthrough of Landesman--Levy on the stable homology of Hurwitz spaces, a novel interpretation of the Frobenius fixed components of Hurwitz spaces in terms of the Brauer group of the stack $BG$ and an interpretation of the number of $\F_q$ points of configuration spaces as a certain Tamagawa volume. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12838 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The leading constant in Malle's conjecture over function fields Santens, Tim Number Theory Algebraic Geometry 14G05 (primary), 11R58, 14D23, 14F22 (secondary) We prove the analogue of Malle's conjecture for the global function field $\F_q(t)$ with $q$ sufficiently large, including a precise formula for the leading constant. The main ingredients are the recent breakthrough of Landesman--Levy on the stable homology of Hurwitz spaces, a novel interpretation of the Frobenius fixed components of Hurwitz spaces in terms of the Brauer group of the stack $BG$ and an interpretation of the number of $\F_q$ points of configuration spaces as a certain Tamagawa volume. |
| title | The leading constant in Malle's conjecture over function fields |
| topic | Number Theory Algebraic Geometry 14G05 (primary), 11R58, 14D23, 14F22 (secondary) |
| url | https://arxiv.org/abs/2512.12838 |