On Beauville's conjectural weak splitting property

We present a recent result on the Chow ring of irreducible symplectic varieties. The main object of interest is Beauville's conjectural weak splitting property, which predicts the injectivity of the cycle class map restricted to a certain subalgebra of the rational Chow ring (the subalgebra generated by divisor classes). For special irreducible symplectic varieties we relate it to a conjecture on the existence of rational Lagrangian brations. After deducing that this implies the weak splitting property in many new cases, we present parts of the proof.