Exercise 109.42.8. Let $A$ be a ring and let $\mathbf{P}^ n_ A = \text{Proj}(A[T_0, \ldots , T_ n])$ be projective space over $A$. Let $F \in A[T_0, \ldots , T_ n]$ be homogeneous of degree $d$. Let $X \subset \mathbf{P}^ n_ A$ be the closed subscheme corresponding to the graded ideal $(F)$ of $A[T_0, \ldots , T_ n]$. What can you say about $H^ i(X, \mathcal{O}_ X)$?

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