# Locally acyclic morphism

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.