A version of Cartan–Nochka's theorem for non-Archimedean holomorphic curves with integrated reduced counting functions
UDC 517.5 Let $\mathbb{K}$ be an algebraically closed field of characteristic $0,$ completed with respect to a non-Archimedean absolute value and let $\mathbb{P}^n(\mathbb{K})$ be an $n$-dimensional projective space over $\mathbb{K}.$ A collection $\mathcal H = \{H_1,\ldots,H_q\} \in \mathbb{P}^n(\m...
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| Datum: | 2026 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8755 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513283039035392 |
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| author | Phuong, Ha Tran Hung, Bui The Inthavichit, Padaphet Phuong, Ha Tran Hung, Bui The Inthavichit, Padaphet |
| author_facet | Phuong, Ha Tran Hung, Bui The Inthavichit, Padaphet Phuong, Ha Tran Hung, Bui The Inthavichit, Padaphet |
| author_sort | Phuong, Ha Tran |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:34:00Z |
| description | UDC 517.5
Let $\mathbb{K}$ be an algebraically closed field of characteristic $0,$ completed with respect to a non-Archimedean absolute value and let $\mathbb{P}^n(\mathbb{K})$ be an $n$-dimensional projective space over $\mathbb{K}.$ A collection $\mathcal H = \{H_1,\ldots,H_q\} \in \mathbb{P}^n(\mathbb{K}),$ $q \geq N+1,$ is said to be in $N$-subgeneral position if, for any $1\leq i_1<\ldots<i_{N+1}\leq q,$ we have $\bigcap_{j=1}^{N+1} H_{i_j} = \varnothing.$ We prove a version of the second main theorem for non-Archimedean holomorphic curves intersecting hyperplanes in $N$-subgeneral position with integrated reduced counting functions. |
| doi_str_mv | 10.3842/umzh.v77i9.8755 |
| first_indexed | 2026-03-24T03:42:13Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8755 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:42:13Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-87552026-03-21T13:34:00Z A version of Cartan–Nochka's theorem for non-Archimedean holomorphic curves with integrated reduced counting functions A version of Cartan–Nochka's theorem for non-Archimedean holomorphic curves with integrated reduced counting functions Phuong, Ha Tran Hung, Bui The Inthavichit, Padaphet Phuong, Ha Tran Hung, Bui The Inthavichit, Padaphet Holomorphic curves, $p$-adic value distribution, $p$-adic Nevanlinna-Cartan theory UDC 517.5 Let $\mathbb{K}$ be an algebraically closed field of characteristic $0,$ completed with respect to a non-Archimedean absolute value and let $\mathbb{P}^n(\mathbb{K})$ be an $n$-dimensional projective space over $\mathbb{K}.$ A collection $\mathcal H = \{H_1,\ldots,H_q\} \in \mathbb{P}^n(\mathbb{K}),$ $q \geq N+1,$ is said to be in $N$-subgeneral position if, for any $1\leq i_1<\ldots<i_{N+1}\leq q,$ we have $\bigcap_{j=1}^{N+1} H_{i_j} = \varnothing.$ We prove a version of the second main theorem for non-Archimedean holomorphic curves intersecting hyperplanes in $N$-subgeneral position with integrated reduced counting functions. УДК 517.5 Версія теореми Картана–Ночки для неархімедових голоморфних кривих із інтегрованими редукованими функціями підрахунку Нехай $\mathbb{K}$ – алгебраїчно замкнене поле характеристики $0$, поповнене щодо неархімедового абсолютного значення, а $\mathbb{P}^n(\mathbb{K})$ – $n$-вимірний проєктивний простір над $\mathbb{K}.$ Кажуть, що множина $\mathcal{H} = {H_1,\ldots,H_q} \subset \mathbb{P}^n(\mathbb{K}),$ де $q \geq N+1,$ розташована у $N$-підзагальному положенні, якщо для будь-яких $1 \leq i_1 < \ldots < i_{N+1} \leq q$ виконується $\bigcap_{j=1}^{N+1} H_{i_j} = \varnothing.$ У цій статті доведено версію другої основної теореми для неархімедових голоморфних кривих, що перетинають гіперплощини у $N$-підзагальному положенні з інтегрованими редукованими функціями підрахунку. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8755 10.3842/umzh.v77i9.8755 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 9 (2025); 595–596 Український математичний журнал; Том 77 № 9 (2025); 595–596 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8755/10566 Copyright (c) 2025 Ha Tran Phuong, Bui The Hung, Padaphet Inthavichit |
| spellingShingle | Phuong, Ha Tran Hung, Bui The Inthavichit, Padaphet Phuong, Ha Tran Hung, Bui The Inthavichit, Padaphet A version of Cartan–Nochka's theorem for non-Archimedean holomorphic curves with integrated reduced counting functions |
| title | A version of Cartan–Nochka's theorem for non-Archimedean holomorphic curves with integrated reduced counting functions |
| title_alt | A version of Cartan–Nochka's theorem for non-Archimedean holomorphic curves with integrated reduced counting functions |
| title_full | A version of Cartan–Nochka's theorem for non-Archimedean holomorphic curves with integrated reduced counting functions |
| title_fullStr | A version of Cartan–Nochka's theorem for non-Archimedean holomorphic curves with integrated reduced counting functions |
| title_full_unstemmed | A version of Cartan–Nochka's theorem for non-Archimedean holomorphic curves with integrated reduced counting functions |
| title_short | A version of Cartan–Nochka's theorem for non-Archimedean holomorphic curves with integrated reduced counting functions |
| title_sort | version of cartan–nochka's theorem for non-archimedean holomorphic curves with integrated reduced counting functions |
| topic_facet | Holomorphic curves $p$-adic value distribution $p$-adic Nevanlinna-Cartan theory |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8755 |
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