On the Rigid Cohomology of Certain Shimura Varieties

2014/11/25 by Michael Harris, Harris, Michael, Kai-Wen Lan +5 · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1411.6717

Version of December 2013

arxiv created 2014/11/25 · arxiv updated 2014/11/26

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.

Cited by

• L-functions of elliptic curves in ring class extensions of real quadratic fields via regularized theta liftings

Related

• Local-global compatibility for l=p, II
• Local-global compatibility for l=p, I
• Galois representations arising from some compact Shimura varieties
• The Local Langlands correspondence for \GL_n over p-adic fields
• Monodromy for some rank two Galois representations over CM fields