2 problems

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Rationality conjecture for the abelian part of an $ell$ -adic representation
Let $K$ and $E\subset\overline{\mathbb{Q}}_\ell$ be number fields, and let $\rho_\ell:\operatorname{Gal}_K\to\mathrm{GL}_n(\overline{\mathbb{Q}}_\ell)$ be a semisimple $E$ -rational…
Conjectureopenabelian-representations algebraic-monodromy-groups galois-representationsarXiv posted 2 days ago
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Compatibility conjecture for abelian parts of compatible systems
Let $E$ be a number field and let $\{\rho_\lambda:\operatorname{Gal}_K\to\mathrm{GL}_n(\overline E_\lambda):\lambda\in\Sigma_E\}$ be a semisimple compatible system of $K$ defined o…
Conjectureopenalgebraic-monodromy-groups compatible-systems galois-representationsarXiv posted 2 days ago

Rationality conjecture for the abelian part of an ellellell-adic representation