# Algebraic monodromy groups of $l$-adic representations of Gal$(\overline{\mathbb{Q}} /\mathbb{Q})$

@article{Tang2019AlgebraicMG,
title={Algebraic monodromy groups of \$l\$-adic representations of Gal\$(\overline\{\mathbb\{Q\}\} /\mathbb\{Q\})\$},
author={Shiang Tang},
journal={Algebra \& Number Theory},
year={2019},
volume={13},
pages={1353-1394}
}
• Shiang Tang
• Published 2019
• Mathematics
• Algebra & Number Theory
A connected reductive algebraic group $G$ is said to be an $l$-adic algebraic monodromy group for $\mathrm{Gal}({\overline{\mathbb Q}}/{\mathbb Q})$ if there is a continuous homomorphism $$\mathrm{Gal}({\overline{\mathbb Q}}/{\mathbb Q}) \to G(\overline{\mathbb Q}_l)$$ with Zariski-dense image. In this paper, we give a classification of connected $l$-adic algebraic monodromy groups for $\mathrm{Gal}({\overline{\mathbb Q}}/{\mathbb Q})$, in particular producing the first such examples for… Expand
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