Are all word-hyperbolic groups residually finite?

Theorem 1.1: there is a torsion-free word-hyperbolic group $G$, the fundamental group of a finite Euclidean triangle complex, that is not residually finite; one member of a fixed finite family of nontrivial elements lies in the finite residual, without identifying which. Corollary 1.2: every finite-dimensional representation of $G$ over every commutative field kills the finite residual, so $G$ is linear over no field. With Kapovich-Wise this gives a nontrivial hyperbolic group with no nontrivial finite quotient and a hyperbolic group that is not virtually torsion-free (curator's reading of the paper's stated consequences). It says nothing about skew fields or infinite-dimensional representations, and does not settle whether all hyperbolic groups are sofic.

Theorem 1.1: there is a torsion-free word-hyperbolic group $G$, the fundamental group of a finite Euclidean triangle complex, that is not residually finite; one member of a fixed finite family of nontrivial elements lies in the finite residual, without identifying which. Corollary 1.2: every finite-dimensional representation of $G$ over every commutative field kills the finite residual, so $G$ is linear over no field. With Kapovich-Wise this gives a nontrivial hyperbolic group with no nontrivial finite quotient and a hyperbolic group that is not virtually torsion-free (curator's reading of the paper's stated consequences). It says nothing about skew fields or infinite-dimensional representations, and does not settle whether all hyperbolic groups are sofic.