Generic vanishing and minimal cohomology classes on abelian fivefolds
  We classify GV-subschemes of five-dimensional ppavs, showing that they exist only on Jacobians of curves and intermediate Jacobians of cubic threefolds, and confirming a conjecture of Pareschi--Popa in this case. The result is implied by a more general statement about subvarieties of minimal cohomology class whose sum is a theta divisor. 
Sebastian Casalaina-Martin, Mihnea Popa, and Stefan Schreieder
math.AG