# Serre’s twisting theorem

Let $X$ be a scheme, and $\U0001d50f$ an ample invertible sheaf on $X$. Then for any coherent sheaf $\mathcal{F}$, and sufficiently large $n$, ${H}^{i}(\mathcal{F}\otimes {\U0001d50f}^{n})=0$, that is, the higher sheaf cohomology of $\mathcal{F}\otimes {\U0001d50f}^{n}$ 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 |