On the Rigid Cohomology of Certain Shimura Varieties
  We construct the compatible system of $l$-adic representations associated to a regular algebraic cuspidal automorphic representation of $GL_n$ over a CM (or totally real) field and check local-global compatibility for the $l$-adic representation away from $l$ and finite number of rational primes above which the CM field or the automorphic representation ramify. The main innovation is that we impose no self-duality hypothesis on the automorphic representation. 
Michael Harris, Kai-Wen Lan, Richard Taylor, Jack Thorne
math.NT