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A branch of algebraic topology concerning the study of cocycles and coboundaries. It is in some sense a dual theory to homology theory. This tag can be further specialized by using it in conjunction with the tags group-cohomology, etale-cohomology, sheaf-cohomology, galois-cohomology, lie-algebra-cohomology, motivic-cohomology, equivariant-cohomology, ...

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"Künneth bigrading" for subsets of $X \times Y$?

In the topology case, it is the Kunneth theorem for excision pair.In the algebraic geometry(etale cohomology) case , it can be reduced to prove that for $Z_1$,$Z_2$(if $Z=Z_1\times Z_2)$and sheaf $Ri_ … theorem is often proved by using Kunneth theorem for excision pair(c.f Milnor's characteristic class ) update: I had thought you just consider the Künneth case.To give the relationship between the cohomology
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