Integrality properties of the Betti moduli space

We study them, in particular showing on a smooth complex quasi-projective variety the existence of $\ell$-adic absolutely irreducible local systems for all $\ell$ the moment there is a complex irreducible topological local system. The proof is purely arithmetic.

This is work in progress with Johan de Jong, relying in part on earlier work with Michael Groechenig.