{"paper":{"title":"On the Weil descent of Artin-Schreier algebraic function fields over finite fields","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Robert Rolland, St\\'ephane Ballet","submitted_at":"2025-05-27T18:29:20Z","abstract_excerpt":"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 $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21656","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.21656/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}