On the Rigid Cohomology of Certain Shimura Varieties

Michael Harris; Kai-Wen Lan; Richard Taylor; Jack Thorne

On the Rigid Cohomology of Certain Shimura Varieties

Number Theory 2014-11-26 v1

Authors: Michael Harris , Kai-Wen Lan , Richard Taylor , Jack Thorne

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.

Keywords

rigid cohomology Shimura varieties $l$-adic representations automorphic representations CM fields local-global compatibility self-duality

Cite

@article{arxiv.1411.6717,
  title  = {On the Rigid Cohomology of Certain Shimura Varieties},
  author = {Michael Harris and Kai-Wen Lan and Richard Taylor and Jack Thorne},
  journal= {arXiv preprint arXiv:1411.6717},
  year   = {2014}
}

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Version of December 2013

On the Rigid Cohomology of Certain Shimura Varieties

Abstract

Keywords

Cite

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