Monodromy for some rank two Galois representations over CM fields

Abstract

We investigate local-global compatibility for cuspidal automorphic representations $\pi$ for GL(2) over CM fields that are regular algebraic of weight $0$. We prove that for a Dirichlet density one set of primes $l$ and any $\iota :{\overline{\mathbf{Q}}}_l\cong \mathbf{C}$, the $l$-adic Galois representation attached to $\pi$ and $\iota$ has nontrivial monodromy at any $v\nmid l$ in $F$ at which $\pi$ is special.

16 pages, refereed version, to appear in Doc. Math. Small correction added to the proof of Lemma 2.3