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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2505.21656 |
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| _version_ | 1866908381930848256 |
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| author | Ballet, Stéphane Rolland, Robert |
| author_facet | Ballet, Stéphane Rolland, Robert |
| contents | Let us consider a generalized Artin-Schreier algebraic function field extension $F$ of the rational function field $\F_{p^n}(x)$ defined over the finite field extension $K=\F_{p^n}$ of the prime field $\F_p$. We assume that $K$ is algebraically closed in $F$. We give general results on the descent over the fields $k= \F_{p^t}$ for $t$ dividing $n$. Then, we completely handle the bi-cyclic case of the descent over the fields $k_1=\F_{p}$ and $k_2= \F_{p^2}$ of all the sub-extensions of $F$ defined over $\F_{p^4}$. We give explicit examples with small prime numbers $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21656 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Weil descent of Artin-Schreier algebraic function fields over finite fields Ballet, Stéphane Rolland, Robert Number Theory 11G20, 14H25 Let us consider a generalized Artin-Schreier algebraic function field extension $F$ of the rational function field $\F_{p^n}(x)$ defined over the finite field extension $K=\F_{p^n}$ of the prime field $\F_p$. We assume that $K$ is algebraically closed in $F$. We give general results on the descent over the fields $k= \F_{p^t}$ for $t$ dividing $n$. Then, we completely handle the bi-cyclic case of the descent over the fields $k_1=\F_{p}$ and $k_2= \F_{p^2}$ of all the sub-extensions of $F$ defined over $\F_{p^4}$. We give explicit examples with small prime numbers $p$. |
| title | On the Weil descent of Artin-Schreier algebraic function fields over finite fields |
| topic | Number Theory 11G20, 14H25 |
| url | https://arxiv.org/abs/2505.21656 |