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 | Statement: [John Tate, notableWork, Tate–Shafarevich group]

Target entity: Tate–Shafarevich group
Context triple: [John Tate, notableWork, Tate–Shafarevich group]

• A. Shafarevich group of a torus chosen
  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.
• B. Mordell–Weil theorem
  The Mordell–Weil theorem is a fundamental result in number theory stating that the group of rational points on an abelian variety (in particular, an elliptic curve) over a number field is finitely generated.
• C. Fontaine–Mazur conjecture
  The Fontaine–Mazur conjecture is a central open problem in number theory that predicts which p-adic Galois representations of number fields arise from geometry or from automorphic forms.
• D. 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.
• E. Faltings' theorem
  Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.