Monodromy for some rank two Galois representations over CM fields

Patrick B. Allen; James Newton

Monodromy for some rank two Galois representations over CM fields

Number Theory 2021-01-25 v3

Authors: Patrick B. Allen , James Newton

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.

Keywords

automorphic representations galois representations galois theory

Cite

@article{arxiv.1901.05490,
  title  = {Monodromy for some rank two Galois representations over CM fields},
  author = {Patrick B. Allen and James Newton},
  journal= {arXiv preprint arXiv:1901.05490},
  year   = {2021}
}

Comments

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

Monodromy for some rank two Galois representations over CM fields

Abstract

Keywords

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