Constructing class fields over local fields
Sebastian Pauli1
1Department of Mathematics and Statistics University of North Carolina Greensboro Greensboro, NC 27402, USA
Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 3, pp. 627-652

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.

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Published online:
DOI: 10.5802/jtnb.563

Sebastian Pauli  1

1 Department of Mathematics and Statistics University of North Carolina Greensboro Greensboro, NC 27402, USA 
Sebastian Pauli. Constructing class fields over local fields. Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 3, pp. 627-652. doi: 10.5802/jtnb.563
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