Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
algebraic groups
abelian varieties algebraic tori |
| gptkbp:definedIn |
gptkb:Weyl_group
Galois module |
| gptkbp:field |
gptkb:algebraic_geometry
algebraic number theory |
| gptkbp:firstCohomology |
classifies torsors
|
| gptkbp:generalizes |
group cohomology
|
| https://www.w3.org/2000/01/rdf-schema#label |
Galois cohomology groups
|
| gptkbp:introduced |
gptkb:Emil_Artin
gptkb:John_Tate |
| gptkbp:notation |
H^n(G, M)
|
| gptkbp:relatedTo |
gptkb:Galois_theory
group cohomology |
| gptkbp:secondCohomology |
classifies central simple algebras
relatedTo Brauer group |
| gptkbp:usedFor |
class field theory
describing obstructions in algebraic structures studying field extensions |
| gptkbp:usedIn |
gptkb:Selmer_groups
gptkb:Hasse_principle gptkb:Kummer_theory gptkb:Weil_group gptkb:Tate–Shafarevich_group gptkb:Tate_cohomology gptkb:étale_cohomology gptkb:Galois_descent classification of quadratic forms motivic cohomology obstruction theory descent theory classification of torsors local-global principles arithmetic duality theorems classification of Brauer groups classification of Galois extensions classification of algebraic K-theory classification of algebraic cycles classification of algebraic groups classification of algebraic structures classification of division algebras classification of field automorphisms classification of field invariants classification of motives classification of principal homogeneous spaces classification of rational points |
| gptkbp:bfsParent |
gptkb:Bloch-Kato_conjecture
|
| gptkbp:bfsLayer |
7
|