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 p∈N, there is a natural isomorphism

HpY(X,F)⊕HpZ(X,F)→HpY∪Z(X,F)

between local cohomology groups. I can obtain this by taking an injective resolution 0→F→I∙ of F, and constructing by hand a

splitexact sequence of complexes of sheaves0→ΓY(X,I∙)→ΓY∪Z(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**

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