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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:appliesTo
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algebraic groups
field extensions
abelian varieties
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gptkbp:citation
|
Tate, John. The cohomology groups of class field theory
Serre, Jean-Pierre. Galois Cohomology
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gptkbp:definedIn
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Galois module
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gptkbp:degree
|
n (integer)
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gptkbp:developedBy
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gptkb:John_Tate
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gptkbp:field
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gptkb:algebra
gptkb:algebraic_geometry
number theory
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gptkbp:firstDegree
|
H^1(G, M)
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gptkbp:generalizes
|
group cohomology
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|
https://www.w3.org/2000/01/rdf-schema#label
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Galois cohomology group
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gptkbp:introduced
|
gptkb:Emil_Artin
|
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gptkbp:notation
|
H^n(G, M)
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gptkbp:relatedTo
|
gptkb:Weyl_group
group cohomology
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gptkbp:secondDegree
|
H^2(G, M)
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gptkbp:studiedBy
|
gptkb:Brauer_group
gptkb:Kummer_theory
gptkb:Tate–Shafarevich_group
gptkb:Tate_cohomology
gptkb:Hilbert's_Theorem_90
gptkb:Selmer_group
gptkb:Weil–Châtelet_group
|
|
gptkbp:studies
|
actions of Galois groups on modules
|
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gptkbp:usedIn
|
gptkb:algebraic_K-theory
class field theory
obstruction theory
descent theory
|
|
gptkbp:usedToClassify
|
torsors
principal homogeneous spaces
|
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gptkbp:zeroDegree
|
H^0(G, M)
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gptkbp:bfsParent
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gptkb:Selmer_group
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gptkbp:bfsLayer
|
6
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