Sur le produit de vari\'et\'es localement factorielles ou Q-factorielles
  We show that the factorial and Q-factorial loci of algebraic varieties defined over an algebraically closed field are open, that products of locally factorial varieties are still locally factorial, and that this property remains true for Q-factorial varieties if the ground field is not the algebraic closure of a finite field. 
Samuel Boissi\`ere, Ofer Gabber, Olivier Serman
math.AG math.AC