Ell-adic Representations Associated to Modular Forms over Imaginary Quadratic Fields

Berger, Tobias and Harcos, Gergely (2007) Ell-adic Representations Associated to Modular Forms over Imaginary Quadratic Fields. International Mathematics Research Notices, 2007. rnm113. ISSN 1073-7928 (print), 1687-0247 (online)

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Abstract

Let p be a regular algebraic cuspidal automorphic representation of GL(2) over an imaginary quadratic number field K, and let l be a prime number. Assuming the central character of p is invariant under the nontrivial automorphism of K, it is shown that there is a continuous irreducible l-adic representation rho of Gal((K) over bar /K) such that L(s, rho(v)) = L(s, pi(v)) whenever v is a prime of K outside an explicit finite set.

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