On projective linear groups over finite fields as Galois groups over the rational numbers

Zusammenfassung

Ideas and techniques from Khare´s and Wintenberger’s preprint on the proof of Serre’s conjecture for odd conductors are used to establish that for a fixed prime l infinitely many of the groups PSL₂(Flr ), PGL₂(Flr ) (for r running) occur as Galois groups over the rationals such that the corresponding number fields are unramified outside a set consisting of l and only one other prime.