Ambrus Pal (Imperial College London): Simpson's conjecture over finite fields 1
We expect that an l-adic Galois representation of the etale fundamental group of a smooth quasi-projective variety should be motivic in origin under mild assumptions. In a joint work with Raju Krishnamoorthy I recently proved
a special case of this conjecture, which characterises all l-adic representations which are coming from elliptic curves. The proof relies on the Langlands correspondence over global function fields and the theory of p-adic coefficients. In my lectures I will introduce these subjects and give an overview of the proof.