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: [Cohomologie Galoisienne, topic, Tate–Shafarevich group]

Target entity: Tate–Shafarevich group
Context triple: [Cohomologie Galoisienne, topic, 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. 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.
• D. 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.
• E. Sato–Tate distribution (for families of elliptic curves)
  The Sato–Tate distribution (for families of elliptic curves) is a probabilistic law describing how the normalized Frobenius traces (or equivalently, the angles in the Hasse bound) of elliptic curves are distributed, typically following a specific sine-squared measure on the interval [0, π].
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.