simpson conjectured that for a reductive group $g$, rigid $g$-local systems on a smooth projective complex variety are integral. i will discuss a proof of integrality for cohomologically rigid $g$-local systems. this generalizes and is inspired by work of esnault and groechenig for $gl_n$. surprisingly, the main tools used in the proof (for general $g$ and $gl_n$) are the work of l. lafforgue on the langlands program for curves over function fields, and work of drinfeld on companions of $\ell$-adic sheaves. the major differences between general $g$ and $gl_n$ are first to make sense of companions for $g$-local systems, and second to show that the monodromy group of a rigid g-local system is semisimple. \\ \\ all work is joint with stefan patrikis.