Tate's theorem on the Galois cohomology of abelian varieties over finite extensions
GPTKB entity
Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:concerns |
gptkb:Galois_cohomology
abelian varieties finite extensions of fields |
| 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 finite extensions
|
| gptkbp:implies |
finiteness of the Tate–Shafarevich group under certain conditions
|
| gptkbp:namedAfter |
gptkb:John_Tate
|
| gptkbp:provenBy |
gptkb:John_Tate
|
| gptkbp:publishedIn |
gptkb:Proceedings_of_the_International_Congress_of_Mathematicians_1966
|
| gptkbp:relatedTo |
gptkb:Tate_module
gptkb:Tate_duality |
| gptkbp:state |
For an abelian variety A over a finite extension K of a global field, the Galois cohomology group H^1(Gal(K^s/K),A) is finite.
|
| gptkbp:yearProved |
1966
|
| gptkbp:bfsParent |
gptkb:John_Torrence_Tate
|
| gptkbp:bfsLayer |
6
|