 Fujita vanishing

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 $a\ge a_0$, and every nef divisor $N$. The uniformity in $N$ is stronger than Serre vanishing. Fujino's note on Fujita vanishing states the theorem for arbitrary projective schemes over a field.