On the Beauville conjecture
  We investigate Beauville's conjecture on the Chow ring of irreducible symplectic varieties. For special irreducible symplectic varieties we relate it to a conjecture on the existence of rational Lagrangian fibrations, which proves Beauville's conjecture in many new cases. We further apply the same techniques to reduce Beauville's conjecture to Picard rank two. 
Ulrike Riess
math.AG