Reference request: local cohomology in disjoint union

I have a topological space X and two disjoint, closed subspaces Y and Z of X. I believe that in this situation, for any abelian sheaf F on X and any pN, there is a natural isomorphism

HpY(X,F)HpZ(X,F)HpYZ(X,F)

between local cohomology groups. I can obtain this by taking an injective resolution 0FI of F, and constructing by hand a split exact sequence of complexes of sheaves

0ΓY(X,I)ΓYZ(X,I)ΓZ(X,I)0

and then passing to cohomology. I am certain that this is completely standard and well known; could someone please point me to a (preferably modern) reference for this result?

Answer

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Source : Link , Question Author : user90358 , Answer Author : Community

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