Privileged ${\mathrm{SL}}_3$-local systems are motivic

Abstract

Let $X$ be a smooth projective variety over the complex numbers, and let $\mathbb{V}$ be an irreducible privileged ${\mathrm{SL}}_3$-local system on $X$ in the sense of Esnault and Groechenig. We show that $\mathbb{V}$ is of geometric origin. We also give an example of a privileged but non-rigid ${\mathrm{SL}}_3$-local system.

arXiv comment20 pages