Tame Galois realizations of GL2(Fℓ)GL2(Fℓ) over QQ

TextThis paper concerns the tame Galois inverse problem. For each prime number ℓ   we construct infinitely many semistable elliptic curves over QQ with good supersingular reduction at ℓ. The Galois action on the ℓ  -torsion points of these elliptic curves provides tame Galois realizations of GL2(Fℓ)GL2(Fℓ) over QQ.VideoFor a video summary of this paper, please visit http://www.youtube.com/watch?v=MsF9OVbPQYU.