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For a continuous map $f:X\to Y$ and a sheaf $\mathcal F$ on $X$, the Leray spectral sequence is
$$
E_2^{p,q}=H^p(Y,R^qf_*\mathcal F)\Longrightarrow H^{p+q}(X,\mathcal F).
$$
If every higher direct image vanishes, its edge maps identify $H^p(X,\mathcal F)$ with $H^p(Y,f_*\mathcal F)$.


Leray spectral sequence

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 126 / 2 / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 126 / 2 / iv / Solution

{wiki=Leray_spectral_sequence}

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.


Leray spectral sequence

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Leray spectral sequence

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