The augmented base locus in positive characteristic
  Let L be a nef line bundle on a projective scheme X in positive characteristic. We prove that the augmented base locus of L is equal to the union of the irreducible closed subsets V of X such that the restriction of L to V is not big. For a smooth variety in characteristic zero, this was proved by Nakamaye using vanishing theorems. 
Paolo Cascini, James McKernan, and Mircea Mustata
math.AG