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.