 Leray spectral sequence

For a continuous map $f:X\to Y$ and a sheaf $\mathcal{F}$ on $X$, the Leray spectral sequence isIf every higher direct image vanishes, its edge maps identify $H^p(X,\mathcal{F})$ with $H^p(Y,f_{\ast }\mathcal{F})$.

The Leray spectral sequence is a mathematical tool used in algebraic topology, specifically in the context of sheaf theory and the study of cohomological properties of spaces. It provides a way to compute the cohomology of a space that can be decomposed into simpler pieces, such as a fibration or a covering.