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

URI: https://gptkb.org/entity/Tate's_theorem_on_the_Galois_cohomology_of_abelian_varieties_over_algebraic_extensions
GPTKB entity
Statements (18)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:author gptkb:John_Tate
gptkbp:concerns gptkb:Galois_cohomology
abelian varieties
algebraic extensions
gptkbp:field gptkb:algebraic_geometry
number theory
gptkbp:implies the Tate-Shafarevich group is finite for abelian varieties over number fields under certain conditions
gptkbp:namedAfter gptkb:John_Tate
gptkbp:publicationYear 1958
gptkbp:publishedIn gptkb:Proceedings_of_the_International_Congress_of_Mathematicians_1958
gptkbp:relatedTo gptkb:Tate_conjecture
gptkb:Tate_module
gptkb:Mordell-Weil_theorem
gptkbp:state For an abelian variety A over a field K, the Galois cohomology group H^1(Gal(K^s/K),A(K^s)) vanishes if K is a finite field or a number field and K^s is a separable closure.
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 extensions