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arXiv · 1411.6717

On the Rigid Cohomology of Certain Shimura Varieties

Michael Harris·Kai-Wen Lan·Richard Taylor·Jack Thorne
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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.

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Michael Harris, Kai-Wen Lan, Richard Taylor, Jack Thorne. 2014-11-25. On the Rigid Cohomology of Certain Shimura Varieties. https://arxiv.org/abs/1411.6717

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