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
Canonical name	SerresTwistingTheorem
Date of creation	2013-03-22 13:52:50
Last modified on	2013-03-22 13:52:50
Owner	bwebste (988)
Last modified by	bwebste (988)
Numerical id	5
Author	bwebste (988)
Entry type	Theorem
Classification	msc 14A99