# 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} }

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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