Explicit construction of integral bases of radical function fields

Qingquan Wu

doi:10.5802/jtnb.714

Qingquan Wu ¹

¹Department of Mathematics and Statistics University of Calgary 2500 University Drive NW Calgary, Alberta T2N 1N4

Journal de théorie des nombres de Bordeaux, Volume 22 (2010) no. 1, pp. 259-270

Abstract (Original language)
Résumé

We give an explicit construction of an integral basis for a radical function field $K = k (t, ρ)$ , where $ρ^{n} = D \in k [t]$ , under the assumptions $[K : k (t)] = n$ and $c h a r (k) ∤ n$ . The field discriminant of $K$ is also computed. We explain why these questions are substantially easier than the corresponding ones in number fields. Some formulae for the $P$ -signatures of a radical function field are also discussed in this paper.

Nous donnons une construction explicite d’une base entière pour le corps de fonction $K = k (t, ρ)$ , où $ρ^{n} = D \in k [t]$ , sous l’hypothèse $[K : k (t)] = n$ et $c h a r (k) ∤ n$ . Le discriminant du corps $K$ est également calculé. Nous expliquons pourquoi ces questions sont considérablement plus faciles que dans le cas des corps de nombres. Quelques formules pour les $P$ -signatures des corps de fonction radiciels sont également présentées dans ce papier.

Article information
Cite this article

Received: 2008-10-21
Published online: 2010-07-19

Zbl MR

DOI: 10.5802/jtnb.714

Author's affiliations:

Qingquan Wu ¹

¹ Department of Mathematics and Statistics University of Calgary 2500 University Drive NW Calgary, Alberta T2N 1N4

Qingquan Wu. Explicit construction of integral bases of radical function fields. Journal de théorie des nombres de Bordeaux, Volume 22 (2010) no. 1, pp. 259-270. doi: 10.5802/jtnb.714

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