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Results tagged with cohomology
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user 90358
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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Reference request: local cohomology in disjoint union
abelian sheaf $\mathcal{F}$ on $X$ and any $p \in \mathbb{N}$, there is a natural isomorphism
$$ H^p_Y(X,\mathcal{F}) \oplus H^p_Z(X, \mathcal{F}) \to H^p_{Y \cup Z}(X, \mathcal{F})$$
between local cohomology … a split exact sequence of complexes of sheaves
$$ 0 \to \Gamma_Y(X,\mathcal{I}^\bullet) \to \Gamma_{Y\cup Z}(X,\mathcal{I}^\bullet) \to \Gamma_Z(X,\mathcal{I}^\bullet) \to 0$$
and then passing to cohomology …
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