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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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What is sheaf cohomology intuitively?

One way to think about $H^1(A)$ is to use the long exact sequence not as a property of cohomology, but outright as a definition. … However, I don't find this very useful for thinking about higher cohomology, since it would need that I somehow understand lower cohomology much better. …
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Is there a direct way to compute the higher derived image sheaves of a family of $\mathbb{P}...

Let $V\rightarrow Y$ be a vector bundle of rank $n+1$ over $Y$, with $Y$ reasonably nice (I care about the case of smooth, irreducible affine). Let $X=\mathbb{P}(V)$ be the projectivization of $V$, so …