A compatible collection of G-representations with full algebraic monodromy at a finite G-good set of primes has full monodromy on a set of primes of Dirichlet density 1, with applications to non-Abelian Shimura varieties.
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Transport of Zariski density in compatible collections of $G$-representations
A compatible collection of G-representations with full algebraic monodromy at a finite G-good set of primes has full monodromy on a set of primes of Dirichlet density 1, with applications to non-Abelian Shimura varieties.