from Čech cohomology to sheaf cohomology. It is always an isomorphism in degrees "n" = 0 and 1, but may fail to be so in general. For the Zariski topology on a Noetherian separated scheme, Čech and sheaf cohomology agree for any quasi-coherent sheaf. For the étale topology, the two cohomologies agree for any étale sheaf on "X", provided that any finite set of points of "X" are contained in some open affine subscheme. This is satisfied, for example, if "X" is quasi-projective over an affine scheme.