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 |
| https://www.w3.org/2000/01/rdf-schema#label |
Tate's theorem on the Galois cohomology of abelian varieties over algebraic extensions
|
| 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
|