Tate's theorem on the Galois cohomology of abelian varieties over finite fields
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
finite fields
|
| gptkbp:citation |
gptkb:Tate,_J._(1966)._Endomorphisms_of_abelian_varieties_over_finite_fields._Invent._Math._2,_134–144.
|
| gptkbp:concerns |
gptkb:Galois_cohomology
abelian varieties |
| 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 fields
|
| gptkbp:implies |
all principal homogeneous spaces for abelian varieties over finite fields are trivial
|
| gptkbp:namedAfter |
gptkb:John_Tate
|
| gptkbp:provenBy |
gptkb:John_Tate
|
| gptkbp:publishedIn |
gptkb:Inventiones_Mathematicae
|
| gptkbp:relatedTo |
gptkb:Tate_conjecture
gptkb:Weil_conjectures |
| gptkbp:state |
The Galois cohomology group H^1(Gal(K^sep/K),A) vanishes for an abelian variety A over a finite field K
|
| gptkbp:yearProved |
1966
|
| gptkbp:bfsParent |
gptkb:John_Torrence_Tate
|
| gptkbp:bfsLayer |
6
|