Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Tate–Shafarevich group of an abelian variety | Statement: [Cassels–Tate pairing, definedOn, Tate–Shafarevich group of an abelian variety]

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Tate–Shafarevich group of an abelian variety
Triple: [Cassels–Tate pairing, definedOn, Tate–Shafarevich group of an abelian variety]

The Tate–Shafarevich group of an abelian variety is an arithmetic invariant measuring the failure of the local-global principle for rational points on the variety, encoding principal homogeneous spaces that are locally but not globally trivial.