A non-solvable Galois extension of \Q ramified at 2 only

2008/11/26 by Dembele, Lassina, Serre, with a supplement by Jean-Pierre · 1 citation
#11-xx #11Gxx #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0811.4379

Abstract

In this paper, we show the existence of a non-solvable Galois extension of \Q which is unramified outside 2. The extension K we construct has degree 2251731094732800=2¹⁹(3⋅ 5⋅ 17⋅ 257)² and has root discriminant δ_K <2^47/8=58.68..., and is totally complex.

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