A non-solvable Galois extension of $ \mathbb{Q}$ ramified at 2 only

Lassina Dembélé

doi:10.1016/j.crma.2008.12.004

Number Theory

A non-solvable Galois extension of

Q

ramified at 2 only
[Une extension galoisienne non résoluble de

Q

ramifiée seulement en 2]

Présenté par : Jean-Pierre Serre

Lassina Dembélé ¹

¹ Institut für Experimentelle Mathematik, Ellernstrasse 29, 45141 Essen, Germany

Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 111-116.

est référencé par Un complément à la Note de Lassina Dembélé “A non-solvable Galois extension of Q ramified at 2 only” [C. R. Acad. Sci. Paris, Ser. I 347 (2009)]

Résumé
Abstract

Dans cette Note, nous démontrons l'existence d'une extension galoisienne non résoluble de $Q$ ramifiée seulement en 2. L'extension K que nous construisons est de degré $2 251 731 094 732 800 = 2^{19} {(3 \cdot 5 \cdot 17 \cdot 257)}^{2}$ et de discriminant normalisé $δ_{K} < 2^{\frac{47}{8}} = 58, 68 \dots$ , et est totalement complexe.

In this Note, we show the existence of a non-solvable Galois extension of $Q$ which is unramified outside 2. The extension K we construct has degree $2 251 731 094 732 800 = 2^{19} {(3 \cdot 5 \cdot 17 \cdot 257)}^{2}$ , it has root discriminant $δ_{K} < 2^{\frac{47}{8}} = 58.68 \dots$ , and is totally complex.

Reçu le : 2008-11-27
Accepté le : 2008-12-10
Publié le : 2009-02-01

DOI : 10.1016/j.crma.2008.12.004

Affiliations des auteurs :

Lassina Dembélé ¹

¹ Institut für Experimentelle Mathematik, Ellernstrasse 29, 45141 Essen, Germany

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     title = {A non-solvable {Galois} extension of $ \mathbb{Q}$ ramified at 2 only},
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     doi = {10.1016/j.crma.2008.12.004},
     language = {en},
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Lassina Dembélé. A non-solvable Galois extension of $ \mathbb{Q}$ ramified at 2 only. Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 111-116. doi : 10.1016/j.crma.2008.12.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.12.004/

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