Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:abbreviation |
gptkb:Sha
|
| gptkbp:appearsIn |
gptkb:Birch_and_Swinnerton-Dyer_conjecture
|
| gptkbp:containsElement |
isomorphism class of torsors
|
| gptkbp:defines |
The Tate-Shafarevich group of an abelian variety A over a number field K is the group of principal homogeneous spaces for A over K that become trivial over every completion of K.
|
| gptkbp:field |
gptkb:algebraic_geometry
number theory |
| gptkbp:introducedIn |
1960s
|
| gptkbp:namedAfter |
gptkb:Igor_Shafarevich
gptkb:John_Tate |
| gptkbp:openProblem |
Finiteness of the Tate-Shafarevich group for elliptic curves over number fields
|
| gptkbp:relatedTo |
gptkb:algebraic_geometry
gptkb:Galois_cohomology gptkb:elliptic_curve principal homogeneous space |
| gptkbp:symbol |
Ш
|
| gptkbp:bfsParent |
gptkb:Tate's_theorem_on_the_Galois_cohomology_of_elliptic_curves
|
| gptkbp:bfsLayer |
7
|
| https://www.w3.org/2000/01/rdf-schema#label |
Tate-Shafarevich group
|