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

  title={Algebraic monodromy groups of \$l\$-adic representations of Gal\$(\overline\{\mathbb\{Q\}\} /\mathbb\{Q\})\$},
  author={Shiang Tang},
  journal={Algebra \& Number Theory},
  • 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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