In algebraic geometry, a morphism 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.
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Jean-Michel Bismut, A Riemann-Roch Theorem in Bott-Chern Cohomology
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References
- Milne, J. S. (1980), Étale cohomology, Princeton Mathematical Series, vol. 33, Princeton, N.J.: Princeton University Press.
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