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: Shafarevich group of a torus | Statement: [Hasse norm theorem, relatedTo, Shafarevich group of a torus]

Target entity: Shafarevich group of a torus
Context triple: [Hasse norm theorem, relatedTo, Shafarevich group of a torus]

• A. Algebraic Groups and Class Fields
  "Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
• B. Grothendieck–Ogg–Shafarevich formula
  The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
• C. Adeles and Algebraic Groups
  "Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
• D. Hasse–Weil bound for abelian varieties
  The Hasse–Weil bound for abelian varieties is a fundamental result in arithmetic geometry that gives sharp estimates for the number of rational points on abelian varieties over finite fields in terms of their dimension and the field size.
• E. Brauer–Manin obstruction
  The Brauer–Manin obstruction is an arithmetic-geometric mechanism using the Brauer group and adelic points to explain failures of the Hasse principle and weak approximation for rational points on varieties.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

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: Shafarevich group of a torus
Triple: [Hasse norm theorem, relatedTo, Shafarevich group of a torus]

The Shafarevich group of a torus is an arithmetic invariant measuring the failure of local-global principles for principal homogeneous spaces under an algebraic torus over a global field.

Target entity: Shafarevich group of a torus
Target entity description: The Shafarevich group of a torus is an arithmetic invariant measuring the failure of local-global principles for principal homogeneous spaces under an algebraic torus over a global field.

• A. Algebraic Groups and Class Fields
  "Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
• B. Grothendieck–Ogg–Shafarevich formula
  The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
• C. Adeles and Algebraic Groups
  "Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
• D. Hasse–Weil bound for abelian varieties
  The Hasse–Weil bound for abelian varieties is a fundamental result in arithmetic geometry that gives sharp estimates for the number of rational points on abelian varieties over finite fields in terms of their dimension and the field size.
• E. Brauer–Manin obstruction
  The Brauer–Manin obstruction is an arithmetic-geometric mechanism using the Brauer group and adelic points to explain failures of the Hasse principle and weak approximation for rational points on varieties.
• F. None of above. chosen