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- Leray_spectral_sequence abstract "In mathematics, the Leray spectral sequence was a pioneering example in homological algebra, introduced in 1946 by Jean Leray. The formulation was of a spectral sequence, expressing the relationship holding in sheaf cohomology between two topological spaces X and Y, and set up by a continuous mappingf:X → Y.At the time of Leray's work, neither of the two concepts involved (spectral sequence, sheaf cohomology) had reached anything like a definitive state. Therefore it is rarely the case that Leray's result is quoted in its original form. After much work, in the seminar of Henri Cartan in particular, a statement was reached of this kind: assuming some hypotheses on X and Y, and a sheaf F on X, there is a direct image sheaff∗Fon Y.There are also higher direct images Rqf∗F.The E2 term of the typical Leray spectral sequence is Hp(Y, Rqf∗F).The required statement is that this abuts to the sheaf cohomologyHr(X, F).In the formulation achieved by Alexander Grothendieck by about 1957, this is the Grothendieck spectral sequence for the composition of two derived functors.Earlier (1948/9) the implications for singular cohomology were extracted as the Serre spectral sequence, which makes no use of sheaves.".
- Leray_spectral_sequence wikiPageExternalLink l058190.htm.
- Leray_spectral_sequence wikiPageID "5174983".
- Leray_spectral_sequence wikiPageRevisionID "572575947".
- Leray_spectral_sequence hasPhotoCollection Leray_spectral_sequence.
- Leray_spectral_sequence subject Category:Continuous_mappings.
- Leray_spectral_sequence subject Category:Sheaf_theory.
- Leray_spectral_sequence subject Category:Spectral_sequences.
- Leray_spectral_sequence type Abstraction100002137.
- Leray_spectral_sequence type Arrangement107938773.
- Leray_spectral_sequence type ContinuousMappings.
- Leray_spectral_sequence type Function113783816.
- Leray_spectral_sequence type Group100031264.
- Leray_spectral_sequence type MathematicalRelation113783581.
- Leray_spectral_sequence type Ordering108456993.
- Leray_spectral_sequence type Relation100031921.
- Leray_spectral_sequence type Sequence108459252.
- Leray_spectral_sequence type Series108457976.
- Leray_spectral_sequence type SpectralSequences.
- Leray_spectral_sequence comment "In mathematics, the Leray spectral sequence was a pioneering example in homological algebra, introduced in 1946 by Jean Leray. The formulation was of a spectral sequence, expressing the relationship holding in sheaf cohomology between two topological spaces X and Y, and set up by a continuous mappingf:X → Y.At the time of Leray's work, neither of the two concepts involved (spectral sequence, sheaf cohomology) had reached anything like a definitive state.".
- Leray_spectral_sequence label "Leray spectral sequence".
- Leray_spectral_sequence sameAs m.0d699p.
- Leray_spectral_sequence sameAs Q6528749.
- Leray_spectral_sequence sameAs Q6528749.
- Leray_spectral_sequence sameAs Leray_spectral_sequence.
- Leray_spectral_sequence wasDerivedFrom Leray_spectral_sequence?oldid=572575947.
- Leray_spectral_sequence isPrimaryTopicOf Leray_spectral_sequence.