## You are here

HomeLeray spectral sequence

## Primary tabs

# Leray spectral sequence

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 $X$, 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 $f_{*}$ is the direct image functor.

Keywords:

Grothendieck spectral sequence, spectral sequence

Related:

GrothendieckSpectralSequence

Type of Math Object:

Theorem

Major Section:

Reference

## Mathematics Subject Classification

18G40*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections