Skyscraper sheaves cohomology Let $X$ be a topological space and $G$ an abelian group. Denote by $\mathcal{S}$ the skyscraper sheaf with  group $G$ at the point $x\in X$. How I can prove that $\mathcal{S}$ has not cohomology, i.e $H^i(X,\mathcal{S})=0, \: \forall i>0$ ?

A skyscraper sheaf is flasque, hence  has no cohomology: Hartshorne Chap. III, Prop.2.5, page 208.
