A $p$-adic Second Main Theorem
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866909209243680768 |
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| author | Huynh, Dinh Tuan |
| author_facet | Huynh, Dinh Tuan |
| contents | Let $\mathbf{K}$ be an algebraically closed field of arbitrary characteristic, complete with respect to a non-archimedean absolute value $|\,|$. We establish a Second Main Theorem type estimate for analytic map $f\colon \mathbf{K}\rightarrow\mathbb{P}^n(\mathbf{K})$ and a family of $n$ hypersurfaces in $\mathbb{P}^n(\mathbf{K})$ intersecting transversally and not all being hyperplanes. This implements the previous work of Levin where the case of all hypersurfaces having degree greater than one was studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14197 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A $p$-adic Second Main Theorem Huynh, Dinh Tuan Complex Variables Number Theory Let $\mathbf{K}$ be an algebraically closed field of arbitrary characteristic, complete with respect to a non-archimedean absolute value $|\,|$. We establish a Second Main Theorem type estimate for analytic map $f\colon \mathbf{K}\rightarrow\mathbb{P}^n(\mathbf{K})$ and a family of $n$ hypersurfaces in $\mathbb{P}^n(\mathbf{K})$ intersecting transversally and not all being hyperplanes. This implements the previous work of Levin where the case of all hypersurfaces having degree greater than one was studied. |
| title | A $p$-adic Second Main Theorem |
| topic | Complex Variables Number Theory |
| url | https://arxiv.org/abs/2405.14197 |