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In algebraic geometry, a morphism \( f: X \to S \) of schemes is said to be locally acyclic if, roughly, any sheaf on S and its restriction to X through f have the same étale cohomology, locally. For example, a smooth morphism is universally locally acyclic.

References

Milne, J. S. (1980), Étale cohomology, Princeton Mathematical Series 33, Princeton, N.J.: Princeton University Press.