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arXiv · 0707.1338

l-Adic representations associated to modular forms over imaginary quadratic fields

Tobias Berger·Gergely Harcos
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Abstract

Let pi be a regular algebraic cuspidal automorphic representation of GL(2) over an imaginary quadratic number field K such that the central character of pi is invariant under the non-trivial automorphism of K. We show that pi is associated with an l-adic Galois representation rho over K such that at each prime of K outside an explicit finite set the Frobenius polynomial of rho agrees with the Hecke polynomial of pi.

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Tobias Berger, Gergely Harcos. 2007-07-09. l-Adic representations associated to modular forms over imaginary quadratic fields. https://doi.org/10.1093/imrn%2Frnm113

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