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 LeraySpectralSequenceForAnAffineMorphism 2013-03-22 14:08:46 2013-03-22 14:08:46 archibal (4430) archibal (4430) 5 archibal (4430) Example msc 14F99 msc 18G40 msc 55T05