Generalized Kummer theory and its applications

Komatsu, Toru

doi:10.5802/ambp.259

Komatsu, Toru ¹

¹ Faculty of Mathematics Kyushu University 6-10-1 Hakozaki Higashiku Fukuoka, 812-8581 Japan

Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 1, pp. 127-138.

Résumé

In this report we study the arithmetic of Rikuna’s generic polynomial for the cyclic group of order $n$ and obtain a generalized Kummer theory. It is useful under the condition that $ζ \notin k$ and $ω \in k$ where $ζ$ is a primitive $n$ -th root of unity and $ω = ζ + ζ^{- 1}$ . In particular, this result with $ζ \in k$ implies the classical Kummer theory. We also present a method for calculating not only the conductor but also the Artin symbols of the cyclic extension which is defined by the Rikuna polynomial.

MR Zbl

DOI : 10.5802/ambp.259

Classification : 11R20, 12E10, 12G05
Mots clés : Generic polynomial, Kummer theory, Artin symbol

Affiliations des auteurs :

Komatsu, Toru ¹

¹ Faculty of Mathematics Kyushu University 6-10-1 Hakozaki Higashiku Fukuoka, 812-8581 Japan

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Komatsu, Toru. Generalized Kummer theory and its applications. Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 1, pp. 127-138. doi : 10.5802/ambp.259. http://archive.numdam.org/articles/10.5802/ambp.259/

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