Let $L$ be a nef and big line bundle on a scheme $X$. It is well known that if $X$ is a projective over a field then the augmented base locus and the exceptional base locus agree. This result is extended to projective schemes over arbitrary excellent Noetherian bases. In particular the result holds in mixed characteristic.
The augmented base locus in positive characteristic
The stable and augmented base locus under finite morphisms
Approximable algebras and a question of Chen
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