Galois realizations of families of projective linear groups via cusp forms

Luis Victor Dieulefait (1)

1 Dept. d'Àlgebra i Geometria

Using results of Ribet on the images of Galois representations attached to modular forms, we realize linear groups as Galois groups over Q. In particular, combining with results of Brumer we prove that there exist infinitely many exponents r for which PXL_2(p^r) are Galois groups over Q for infinitely many primes p, where PXL means PSL or PGL. (Note: this paper dates from 1998, it is the author's first research work as a PhD student, before the thesis).

Mots clés: Galois representations; Inverse Galois Problem; modular forms

Domaines: Théorie des nombres [math.NT]

Luis Victor Dieulefait. Galois realizations of families of projective linear groups via cusp forms. 1998. ⟨hal-00147919⟩