Constructing class fields over local fields

Sebastian Pauli

doi:10.5802/jtnb.563

Sebastian Pauli ¹

¹ Department of Mathematics and Statistics University of North Carolina Greensboro Greensboro, NC 27402, USA

Journal de théorie des nombres de Bordeaux, Tome 18 (2006) no. 3, pp. 627-652.

Abstract (VO)
Résumé

Let $K$ be a $𝔭$ -adic field. We give an explicit characterization of the abelian extensions of $K$ of degree $p$ by relating the coefficients of the generating polynomials of extensions $L / K$ of degree $p$ to the exponents of generators of the norm group $N_{L / K} (L^{*})$ . This is applied in an algorithm for the construction of class fields of degree $p^{m}$ , which yields an algorithm for the computation of class fields in general.

Soit $K$ un corps $𝔭$ -adique. Nous donnons une caractérisation explicite des extensions abéliennes de $K$ de degré $p$ en reliant les coefficients des polynômes engendrant les extensions $L / K$ de degré $p$ aux exposants des générateurs du groupe des normes $N_{L / K} (L^{*})$ . Ceci est appliqué à un algorithme de construction des corps de classes de degré $p^{m}$ , ce qui conduit à un algorithme de calcul des corps de classes en général.

MR Zbl

DOI : 10.5802/jtnb.563

Affiliations des auteurs :

Sebastian Pauli ¹

¹ Department of Mathematics and Statistics University of North Carolina Greensboro Greensboro, NC 27402, USA

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     volume = {18},
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Sebastian Pauli. Constructing class fields over local fields. Journal de théorie des nombres de Bordeaux, Tome 18 (2006) no. 3, pp. 627-652. doi : 10.5802/jtnb.563. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.563/

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