Tame Galois realizations of GL 2 ( F ` ) over Q 1

This paper concerns the tame inverse Galois problem. For each prime number ` we construct infinitely many semistable elliptic curves over Q with good supersingular reduction at `. The Galois action on the `-torsion points of these elliptic curves provides tame Galois realizations of GL2(F`) over Q.