Let X be a smooth complex projective variety and A an abelian group. Degree i unramified cohomology H i nr(X,A) of X with coefficients in A can be defined as the direct limit of the sets of data αk ∈ H i B(Uk, A), αk|Uk∩Ul = αl|Uk∩Ul , where the Uk’s are sufficiently small Zariski open sets covering X. Here the notation H i B stands for Betti cohomology of the underlying complex analytic space....