# Leray spectral sequence for an affine morphism

Let $f:X\to Y$ be an affine morphism of schemes (that is, every point has an affine neighborhood^{} whose preimage is affine). Then ${R}^{i}{f}_{*}=0$ for every $i>0$, and the Leray spectral sequence tells us that

$${H}^{i}(X,\mathcal{F})={H}^{i}(Y,{f}_{*}\mathcal{F}).$$ |

Title | Leray spectral sequence for an affine morphism |
---|---|

Canonical name | LeraySpectralSequenceForAnAffineMorphism |

Date of creation | 2013-03-22 14:08:46 |

Last modified on | 2013-03-22 14:08:46 |

Owner | archibal (4430) |

Last modified by | archibal (4430) |

Numerical id | 5 |

Author | archibal (4430) |

Entry type | Example |

Classification | msc 14F99 |

Classification | msc 18G40 |

Classification | msc 55T05 |