PlanetMath: Leray spectral sequence

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Leray spectral sequence

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The Leray spectral sequence is a special case of the Grothendieck spectral sequence regarding composition of functors.

If $f : X\to Y$ is a continuous map of topological spaces, and if $\mathcal{F}$ is a sheaf of abelian groups on , then there is a spectral sequence, called the Leray spectral sequence, given by

$E_2^{pq} = H^p(Y,{\rm R}^q f_* \mathcal{F})\implies H^{p+q}(X,\mathcal{F})$

where is the direct image functor.

"Leray spectral sequence" is owned by bwebste. [ full author list (2) | owner history (4) ]

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Keywords:

Grothendieck spectral sequence, spectral sequence

Attachments:: Leray spectral sequence for an affine morphism (Example) by archibal

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Cross-references: direct image, spectral sequence, abelian groups, sheaf, topological spaces, continuous map, functors, composition, Grothendieck spectral sequence
There are 3 references to this entry.

This is version 3 of Leray spectral sequence, born on 2001-12-12, modified 2004-03-31.
Object id is 1099, canonical name is LeraySpectralSequence.
Accessed 3586 times total.

Classification:

18G40 (Category theory; homological algebra :: Homological algebra :: Spectral sequences, hypercohomology)

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