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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:appliesTo
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Schemes
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gptkbp:field
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gptkb:Algebraic_geometry
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gptkbp:firstAppearance
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1960s
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gptkbp:generalizes
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gptkb:Singular_cohomology
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https://www.w3.org/2000/01/rdf-schema#label
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Etale cohomology
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gptkbp:introduced
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gptkb:Alexander_Grothendieck
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gptkbp:notableAchievement
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Proof of Weil conjectures by Pierre Deligne
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gptkbp:notableIdea
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gptkb:Brauer_group
gptkb:Picard_group
gptkb:Poincaré_duality
gptkb:Tate_module
gptkb:Étale_cohomology_with_compact_support
gptkb:Étale_morphism
gptkb:Étale_site
gptkb:Artin–Verdier_duality
gptkb:Chern_class
gptkb:Etale_fundamental_group
gptkb:Etale_sheaf
gptkb:Finiteness_theorem
gptkb:Grothendieck's_six_operations
gptkb:Gysin_sequence
gptkb:Kummer_sequence
gptkb:L-adic_cohomology
gptkb:Lefschetz_trace_formula
gptkb:Leray_spectral_sequence
gptkb:Smooth_base_change_theorem
Grothendieck topology
Cohomological dimension
Comparison theorem
Comparison with Betti cohomology
Comparison with de Rham cohomology
Cycle class map
Proper base change theorem
Torsion sheaf
Étale cohomology of abelian varieties
Étale cohomology of curves
Étale cohomology of elliptic curves
Étale cohomology of fields
Étale cohomology of higher-dimensional varieties
Étale cohomology of surfaces
Étale cohomology with coefficients
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gptkbp:relatedTo
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gptkb:Algebraic_topology
gptkb:Sheaf_cohomology
gptkb:Galois_cohomology
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gptkbp:usedFor
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Proving Weil conjectures
Studying algebraic varieties
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gptkbp:uses
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gptkb:Etale_topology
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gptkbp:bfsParent
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gptkb:algebraic_geometry
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gptkbp:bfsLayer
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5
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