A complement to the note by Lassina Dembélé “A non-solvable Galois extension of \(\mathbb Q\) ramified at 2 only”. (Un complément à la note de Lassina Dembélé.) (French) Zbl 1167.11041
In the previous paper by L. Dembélé [C. R., Math., Acad. Sci. Paris 347, No. 3–4, 111–116 (2009; Zbl 1166.11038)], the degree of the exhibited extension \(K/\mathbb Q\) is high: \([K: \mathbb Q]= 2^{19}(3.5.17.257)^2\), while the root discriminant of \(K\) is small: \(\delta_K< 58,688\ldots\). This majoration already improves best known examples by F. Hajir and C. Maire [J. Symb. Comput. 33, No. 4, 415–423 (2002; Zbl 1086.11051)]. Here, in a few elegant lines, Serre brings down the bound to \(\delta_K< 55,304388\ldots\).
Reviewer: Richard Massy (Valenciennes)
MSC:
| 11R32 | Galois theory |
| 11F80 | Galois representations |
| 11R29 | Class numbers, class groups, discriminants |
