Fujita vanishing
= Fujita vanishing
{c}
Given a <coherent sheaf> $\mathcal F$ and an <ample Cartier divisor> $A$ on a <projective scheme>, one integer $a_0$ ensures $H^i(X,\mathcal F(aA+N))=0$ for all $i>0$, all $a\geq a_0$, and every <nef divisor> $N$. The uniformity in $N$ is stronger than <Serre vanishing>. https://www.math.kyoto-u.ac.jp/~fujino/fujita-vani3.pdf[Fujino's note on Fujita vanishing] states the theorem for arbitrary projective schemes over a field.