Titre :

Théorème d'irréductibilité de Hilbert, conjecture de Malle et problème de Grunwald

Auteur(s) :

Motte, François [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Discipline(s) HAL :

Mathématiques [math]/Théorie des nombres [math.NT]
Mathématiques [math]/Géométrie algébrique [math.AG]

Résumé en anglais : [en]

The central result is a new explicit version of the Hilbert Irreducibility Theorem. Then, starting from a regular Galois extension F/K(T), we can count the number of specialized extensions F_{t_0}/K and not only the ...
Lire la suite >The central result is a new explicit version of the Hilbert Irreducibility Theorem. Then, starting from a regular Galois extension F/K(T), we can count the number of specialized extensions F_{t_0}/K and not only the specialization points t_0, and provide some control of N_{K/Q}(d_{F_{t_0}}) Consequently, we contribute to the Malle conjecture on the number N(K,G,y) of finite Galois extensions E of some number field K of finite group G and of ideal discriminant of norm N_{K/Q}(d_E)< y. For every number field K containing a certain number field K_0 (depending on G), we establish this lower bound : N(K,G,y) <y^{\alpha (G)} for y large enough and some specific exponent \alpha (G) depending on G. We can also prescribe the local behaviour of the specialized extensions at some primes. We deduce new results on the local-global Grunwald problem, in particular for some non-solvable groups G.Lire moins >

Langue :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL