The genus fields of Artin-Schreier extensions

2009/06/25 by Hu, Su, Li, Yan
#11R58 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0906.4626

Abstract

Let q be a power of a prime number p. Let k=\mathbbF_q(t) be the rational function field with constant field \mathbbF_q. Let K=k(α) be an Artin-Schreier extension of k. In this paper, we explicitly describe the ambiguous ideal classes and the genus field of K . Using these results we study the p-part of the ideal class group of the integral closure of \mathbbF_q[t] in K. And we also give an analogy of R\acuteedei-Reichardt's formulae for K.

Related

• Extended genus field of cyclic Kummer extensions of rational function fields
• Genus Field and Extended Genus Field of an Elementary Abelian Extension of Global Fields
• Genus Fields of Congruence Function Fields
• On the arithmetic of Z_p-extensions
• Extended genus fields of abelian extensions of rational function fields