Vanishing of Quasi-Coherent Sheaf Cohomology of Noetherian Affine Scheme

Theorem
Let $X = \operatorname{Spec}(A)$ be the spectrum of a noetherian commutative ring $A$.

Let $\FF$ be a quasi-coherent sheaf on $X$.

Then for all $i \in \Z$ with $i > 0$ the $i$-th sheaf cohomology $H^i(X,\FF) = 0$.

Proof 2
This is a special case of Vanishing of Quasi-Coherent Sheaf Cohomology of Affine Scheme.