In algebraic geometry, a morphism f : X → S {\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.
In algebraic geometry, a morphism f : X → S {\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.
Source: Wikipedia "Locally acyclic morphism" · CC BY-SA 4.0
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