Tate's theorem on the Galois cohomology of abelian varieties over algebraic fields

URI: https://gptkb.org/entity/Tate's_theorem_on_the_Galois_cohomology_of_abelian_varieties_over_algebraic_fields
GPTKB entity
Statements (18)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:author gptkb:John_Tate
gptkbp:concerns gptkb:Galois_cohomology
abelian varieties
algebraic fields
gptkbp:field gptkb:algebraic_geometry
number theory
gptkbp:implies gptkb:Tate_conjecture_for_abelian_varieties_over_finite_fields
gptkbp:namedAfter gptkb:John_Tate
gptkbp:publishedIn gptkb:Proceedings_of_the_International_Congress_of_Mathematicians_1966
gptkbp:relatedTo gptkb:Frobenius_endomorphism
gptkb:Weil_conjectures
gptkb:Tate_module
gptkbp:state For an abelian variety A over a finite field k, the natural map from Hom(A,B)⊗Zl to Hom_Gal(Gal(k^sep/k))(TlA,TlB) is an isomorphism for l≠char(k).
gptkbp:yearProved 1966
gptkbp:bfsParent gptkb:John_Torrence_Tate
gptkbp:bfsLayer 6
https://www.w3.org/2000/01/rdf-schema#label Tate's theorem on the Galois cohomology of abelian varieties over algebraic fields