Tate–Shafarevich group

E1711508 UNEXPLORED

The Tate–Shafarevich group is an arithmetic invariant of an abelian variety (notably an elliptic curve) over a number field that measures the failure of the local-global principle for its rational points.

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All labels observed (7)

Label Occurrences
Tate–Shafarevich group canonical 3
Shafarevich–Tate group 1
Shafarevich–Tate groups 1

Referenced by (9)

Full triples — surface form annotated when it differs from this entity's canonical label.

Cassels–Tate pairing → definedOn → Tate–Shafarevich group ⓘ
Cassels–Tate pairing → definedOn → Tate–Shafarevich group of an abelian variety over a number field ⓘ
linked to: Tate–Shafarevich group
Cassels–Tate pairing → domain → Tate–Shafarevich group × Tate–Shafarevich group ⓘ
linked to: Tate–Shafarevich group
Cassels–Tate pairing → associatedWith → Tate–Shafarevich group of an elliptic curve ⓘ
linked to: Tate–Shafarevich group
Igor Shafarevich → notableIdea → Shafarevich–Tate group ⓘ
linked to: Tate–Shafarevich group
Shafarevich group of a torus → relatedTo → Tate–Shafarevich group ⓘ
Galois cohomology → hasKeyConcept → Tate–Shafarevich group ⓘ
Poitou–Tate duality → involves → Tate–Shafarevich groups ⓘ
linked to: Tate–Shafarevich group
Cohomologie Galoisienne → usedFor → Shafarevich–Tate groups ⓘ
subject linked to: CG
linked to: Tate–Shafarevich group