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Article Dans Une Revue Compositio Mathematica Année : 2018

Rank 3 rigid representations of projective fundamental groups

Résumé

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.

Dates et versions

hal-01335367 , version 1 (21-06-2016)

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Adrian Langer, Carlos T. Simpson. Rank 3 rigid representations of projective fundamental groups. Compositio Mathematica, 2018, 154 (7), pp.1534-1570. ⟨10.1112/S0010437X18007182⟩. ⟨hal-01335367⟩
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