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.
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For a continuous map and a sheaf on , the Leray spectral sequence isIf every higher direct image vanishes, its edge maps identify with .