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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2019
- DOI:
- 10.48550/arXiv.1901.05490
- arXiv:
- arXiv:1901.05490
- Bibcode:
- 2019arXiv190105490A
- Keywords:
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- Mathematics - Number Theory
- E-Print:
- 16 pages, refereed version, to appear in Doc. Math. Small correction added to the proof of Lemma 2.3