Definition 33.35.7. Let k be a field. Let n \geq 0. Let \mathcal{F} be a coherent sheaf on \mathbf{P}^ n_ k. We say \mathcal{F} is m-regular if
H^ i(\mathbf{P}^ n_ k, \mathcal{F}(m - i)) = 0
for i = 1, \ldots , n.
Definition 33.35.7. Let k be a field. Let n \geq 0. Let \mathcal{F} be a coherent sheaf on \mathbf{P}^ n_ k. We say \mathcal{F} is m-regular if
for i = 1, \ldots , n.
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