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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:appliesTo
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Sheaves on schemes
Sheaves on topological spaces
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gptkbp:computes
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Obstructions to solving local-to-global problems
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gptkbp:field
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gptkb:Topology
gptkb:Algebraic_geometry
Homological algebra
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gptkbp:first_cohomology_group
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Classifies extensions of sheaves
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gptkbp:generalizes
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gptkb:Čech_cohomology
gptkb:Singular_cohomology
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gptkbp:higher_cohomology_groups
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Measure failure of exactness
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https://www.w3.org/2000/01/rdf-schema#label
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Sheaf cohomology
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gptkbp:importantFor
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gptkb:Brauer_group
gptkb:Picard_group
gptkb:Deformation_theory
gptkb:Grothendieck's_six_operations
gptkb:Intersection_theory
gptkb:Leray's_theorem
gptkb:Local_cohomology
gptkb:Obstruction_theory
gptkb:Torsors
Classification of vector bundles
Base change theorems
Classification of line bundles
Classification of principal bundles
Cohomological dimension
Cohomology with supports
Duality theorems
Flat base change
Proper base change
Sheaf extensions
Sheaf resolutions
Vanishing theorems
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gptkbp:introduced
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gptkb:Jean_Leray
1940s
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gptkbp:notation
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H^i(X, F)
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gptkbp:relatedTo
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gptkb:Ext_functor
gptkb:Spectral_sequences
Derived functors
|
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gptkbp:tool_for
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gptkb:Number_theory
gptkb:Algebraic_geometry
Complex geometry
|
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gptkbp:used_in
|
gptkb:Algebraic_topology
gptkb:Riemann–Roch_theorem
gptkb:Hodge_theory
gptkb:Serre_duality
gptkb:Étale_cohomology
gptkb:De_Rham_cohomology
gptkb:Leray_spectral_sequence
Grothendieck's theory of schemes
|
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gptkbp:usedFor
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Studying global properties of sheaves
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gptkbp:zero-th_cohomology_group
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Global sections of a sheaf
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gptkbp:bfsParent
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gptkb:Riemann-Roch's_theorem_in_characteristic_p
gptkb:algebraic_geometry
|
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gptkbp:bfsLayer
|
5
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