Wild Stacky Curves and Rings of Mod p Modular Forms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911201710047232 |
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| author | Kobin, Andrew Zureick-Brown, David |
| author_facet | Kobin, Andrew Zureick-Brown, David |
| contents | We extend work of Voight and the second author to compute the log canonical ring of a wild stacky curve over a field of characteristic $p > 0$, which allows us to compute rings of mod $p$ modular forms of level $Γ_{0}(N)$. Our approach also reveals that in characteristics $2$ and $3$, there are infinitely many levels $N$ for which there are weight $2$ modular forms of level $Γ_{0}(N)$ that do not lift to characteristic $0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wild Stacky Curves and Rings of Mod p Modular Forms Kobin, Andrew Zureick-Brown, David Algebraic Geometry Number Theory 14Q05, 14D23, 11F11, 11F33, 11S15 We extend work of Voight and the second author to compute the log canonical ring of a wild stacky curve over a field of characteristic $p > 0$, which allows us to compute rings of mod $p$ modular forms of level $Γ_{0}(N)$. Our approach also reveals that in characteristics $2$ and $3$, there are infinitely many levels $N$ for which there are weight $2$ modular forms of level $Γ_{0}(N)$ that do not lift to characteristic $0$. |
| title | Wild Stacky Curves and Rings of Mod p Modular Forms |
| topic | Algebraic Geometry Number Theory 14Q05, 14D23, 11F11, 11F33, 11S15 |
| url | https://arxiv.org/abs/2510.08821 |