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On the Rigid Cohomology of Certain Shimura Varieties (1411.6717v1)
Published 25 Nov 2014 in math.NT
Abstract: 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.