Displaying similar documents to “Nonsolvable nonic number fields ramified only at one small prime”

PSL ( 2 , 7 ) septimic fields with a power basis

Melisa J. Lavallee, Blair K. Spearman, Qiduan Yang (2012)

Journal de Théorie des Nombres de Bordeaux

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We give an infinite set of distinct monogenic septimic fields whose normal closure has Galois group P S L ( 2 , 7 ) .

PAC fields over number fields

Moshe Jarden (2006)

Journal de Théorie des Nombres de Bordeaux

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We prove that if K is a number field and N is a Galois extension of ℚ which is not algebraically closed, then N is not PAC over K .

Galois Covers and the Hilbert-Grunwald Property

Pierre Dèbes, Nour Ghazi (2012)

Annales de l’institut Fourier

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Our main result combines three topics: it contains a Grunwald-Wang type conclusion, a version of Hilbert’s irreducibility theorem and a p -adic form à la Harbater, but with good reduction, of the Regular Inverse Galois Problem. As a consequence we obtain a statement that questions the RIGP over ℚ . The general strategy is to study and exploit the good reduction of certain twisted models of the covers and of the associated moduli spaces.

Asymptotics of number fields and the Cohen–Lenstra heuristics

Jürgen Klüners (2006)

Journal de Théorie des Nombres de Bordeaux

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We study the asymptotics conjecture of Malle for dihedral groups D ℓ of order 2 ℓ , where ℓ is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen–Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.