On the Weil descent of Artin-Schreier algebraic function fields over finite fields

2025/05/27 by Stéphane Ballet, Ballet, Stéphane, Robert Rolland +1
Mathematics · #11G20 #14H25 #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2505.21656

openalex publication_date 2025/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let us consider a generalized Artin-Schreier algebraic function field extension F of the rational function field \F_pⁿ(x) defined over the finite field extension K=\F_pⁿ 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 k₁=\F_p and k₂= \F_p² of all the sub-extensions of F defined over \F_p⁴. We give explicit examples with small prime numbers p.

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