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Rank 3 rigid representations of projective fundamental groups

  • Adrian Langer (a1) and Carlos Simpson (a2)

Let $X$ be a smooth complex projective variety with basepoint $x$ . We prove that every rigid integral irreducible representation $\unicode[STIX]{x1D70B}_{1}(X\!,x)\rightarrow \operatorname{SL}(3,\mathbb{C})$ is of geometric origin, i.e., it comes from some family of smooth projective varieties. This partially generalizes an earlier result by Corlette and the second author in the rank 2 case and answers one of their questions.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
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