Singular spaces with trivial canonical class

The Beauville-Bogomolov decomposition theorem asserts that any compact Kähler manifold with trivial canonical bundle is finitely covered by the product of a compact complex torus, simply connected Calabi-Yau manifolds, and simply connected irreducible holomorphic symplectic manifolds. The decomposition of the étale cover corresponds to a decomposition of the tangent bundle into a direct sum, whose summands are integrable and stable with respect to any polarization. Building on recent extension theorems for differential forms on singular spaces, in the talk I will sketch the proof of an analogous decomposition theorem for the tangent sheaf of a projective variety with canonical singularities and numerically trivial canonical class. This is joint work with Stefan Kebekus and Thomas Peternell.