30.8.1.1

\begin{equation} \label{coherent-equation-identify} H^ q(\mathbf{P}^ n, \mathcal{O}_{\mathbf{P}^ n_ R}(d)) = \left\{ \begin{matrix} (R[T_0, \ldots , T_ n])_ d
& \text{if}
& q = 0
\\ 0
& \text{if}
& q \not= 0, n
\\ \mathop{\mathrm{Hom}}\nolimits _ R((R[T_0, \ldots , T_ n])_{-n - 1 - d}, R)
& \text{if}
& q = n
\end{matrix} \right. \end{equation}

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