Let X be a smooth complex projective variety with basepoint x. We prove that every rigid integral irreducible representation $\pi_1(X,x)\to SL (3,{ \mathbb C})$ is of geometric origin, i.e., it comes from some family of smooth projective varieties. This partially generalizes an earlier result by K. Corlette and the second author in the rank 2 case and answers one of their questions.
Categories: math.AG