Study and computation of a Hurwitz space and totally real PSL_2(F_8)-extensions of Q
Résumé
Developing on works by Fried, V\"{o}lklein, Matzat, Malle, Débes, Wewers, we give a method for computing a Hurwitz space and illustrate it on some example of number theoristic interest: we study and compute a family of degree~$9$ covers of~$\PP^1_\CC$ with monodromy group~$PSL_2(\FF_8)$ and having four branch points. We deduce explicit regular~$PSL_2(\FF_8)$-extensions of the rational function field~$\QQ(\varphi)$ with totally real fibers. This gives rise to totally real polynomials over~$\QQ$ with Galois group~$PSL_2(\FF_8)$.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)
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