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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 L| V is not big. For a smooth variety in characteristic zero, this was proved by Nakamaye using vanishing theorems. ) = 0. When X is a smooth projective variety in characteristic zero, the above theorem was proved in , making use of the Kawamata-Viehweg vanishing theorem. It is an interestingdoi:10.1017/s0013091513000916 fatcat:52ovnvajofeg7nzpmnsagphvmm