# Serre’s twisting theorem

Let $X$ be a scheme, and $\mathfrak{L}$ an ample invertible sheaf on $X$. Then for any coherent sheaf $\mathcal{F}$, and sufficiently large $n$, $H^{i}(\mathcal{F}\otimes\mathfrak{L}^{n})=0$, that is, the higher sheaf cohomology of $\mathcal{F}\otimes\mathfrak{L}^{n}$ is trivial.

Title Serre’s twisting theorem SerresTwistingTheorem 2013-03-22 13:52:50 2013-03-22 13:52:50 bwebste (988) bwebste (988) 5 bwebste (988) Theorem msc 14A99