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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:appliesTo
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gptkb:Topological_spaces
Schemes
Sheaves
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gptkbp:field
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gptkb:Topology
gptkb:Algebraic_geometry
Homological algebra
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gptkbp:firstCohomologyGroup
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Classifies extensions of sheaves
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gptkbp:generalizes
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gptkb:Čech_cohomology
gptkb:Singular_cohomology
gptkb:Hypercohomology
Non-abelian cohomology
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gptkbp:hasApplication
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gptkb:Kodaira_vanishing_theorem
gptkb:Grothendieck_duality
gptkb:Leray_spectral_sequence
gptkb:Serre's_GAGA_principle
Classification of line bundles
Vanishing theorems
Brauer group computation
Calculation of Betti numbers
Picard group computation
Proof of Weil conjectures
Torsion phenomena in topology
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gptkbp:higherCohomologyGroups
|
Obstructions to gluing local data
|
|
https://www.w3.org/2000/01/rdf-schema#label
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Sheaf Cohomology
|
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gptkbp:importantFor
|
gptkb:Hodge_theory
gptkb:Étale_cohomology
gptkb:Deformation_theory
gptkb:Sheaf_theory
Complex manifolds
D-module theory
Algebraic stacks
|
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gptkbp:introduced
|
gptkb:Jean_Leray
|
|
gptkbp:introducedIn
|
1940s
|
|
gptkbp:notableTool
|
gptkb:Riemann–Roch_theorem
gptkb:Serre_duality
gptkb:Obstruction_theory
Classification of vector bundles
Studying global sections
|
|
gptkbp:notation
|
H^i(X, F)
H^i(X, F)
|
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gptkbp:relatedTo
|
gptkb:Ext_functor
gptkb:Spectral_sequences
gptkb:Grothendieck's_theory
Derived functors
|
|
gptkbp:usedIn
|
gptkb:Algebraic_topology
gptkb:Algebraic_geometry
Complex geometry
|
|
gptkbp:zeroCohomologyGroup
|
Global sections
|
|
gptkbp:bfsParent
|
gptkb:Singular_Homology_Theory
|
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gptkbp:bfsLayer
|
7
|