On the classification of rank two representations of quasiprojective fundamental groups
Résumé
Suppose $X$ is a smooth quasiprojective variety over $\cc$ and $\rho : \pi _1(X,x) \rightarrow SL(2,\cc )$ is a Zariski-dense representation with quasiunipotent monodromy at infinity. Then $\rho$ factors through a map $X\rightarrow Y$ with $Y$ either a DM-curve or a Shimura modular stack.
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