In algebraic geometry, a morphism ${\displaystyle f:X\to S}$ 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, vol. 33, Princeton, N.J.: Princeton University Press.