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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.19533 |
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| _version_ | 1866909980499640320 |
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| author | Matignon, Michel Pagot, Guillaume Turchetti, Daniele |
| author_facet | Matignon, Michel Pagot, Guillaume Turchetti, Daniele |
| contents | Let $p$ be a prime number. Motivated by the local lifting problem for $(\mathbb{Z}/p\mathbb{Z})^n$ with $n>1$, we prove several new results on certain $\mathbb{F}_p$-vector spaces of logarithmic differential forms on the projective line in characteristic $p$, called "spaces $L_{m+1,n}$". Expanding the previous work by the first two authors, we prove positive and negative results for the existence of spaces $L_{m+1,n}$ in many situations. Moreover, we classify all spaces $L_{4p,2}$ for any $p$, and all spaces $L_{15,2}$ for $p=3$. Among the novel tools we use, Moore determinants and computational algebra play a prominent role. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19533 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the arithmetic and geometry of spaces $L_{m+1,n}$ Matignon, Michel Pagot, Guillaume Turchetti, Daniele Number Theory Commutative Algebra Algebraic Geometry 13A50, 14G17 Let $p$ be a prime number. Motivated by the local lifting problem for $(\mathbb{Z}/p\mathbb{Z})^n$ with $n>1$, we prove several new results on certain $\mathbb{F}_p$-vector spaces of logarithmic differential forms on the projective line in characteristic $p$, called "spaces $L_{m+1,n}$". Expanding the previous work by the first two authors, we prove positive and negative results for the existence of spaces $L_{m+1,n}$ in many situations. Moreover, we classify all spaces $L_{4p,2}$ for any $p$, and all spaces $L_{15,2}$ for $p=3$. Among the novel tools we use, Moore determinants and computational algebra play a prominent role. |
| title | On the arithmetic and geometry of spaces $L_{m+1,n}$ |
| topic | Number Theory Commutative Algebra Algebraic Geometry 13A50, 14G17 |
| url | https://arxiv.org/abs/2503.19533 |