# Rank 3 rigid representations of projective fundamental groups

Abstract : Let $X$ be a smooth complex projective variety with basepoint $x$. We prove that every rigid integral irreducible representation $\pi_1(X ,x)\to SL (3, C)$ 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.
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Journal articles

https://hal.archives-ouvertes.fr/hal-01335367
Contributor : Carlos Simpson <>
Submitted on : Tuesday, June 21, 2016 - 9:20:10 PM
Last modification on : Tuesday, December 8, 2020 - 9:59:26 AM

### Identifiers

• HAL Id : hal-01335367, version 1
• ARXIV : 1604.03252

### Citation

Adrian Langer, Carlos Simpson. Rank 3 rigid representations of projective fundamental groups. Compositio Mathematica, Foundation Compositio Mathematica, 2018, 154 (7), pp.1534-1570. ⟨hal-01335367⟩

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