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: Vojta’s conjectures | Statement: [abc conjecture, relatedTo, Vojta’s conjectures]

Target entity: Vojta’s conjectures
Context triple: [abc conjecture, relatedTo, Vojta’s conjectures]

• A. Shafarevich conjecture for abelian varieties
  The Shafarevich conjecture for abelian varieties is a finiteness statement predicting that, over a number field, there are only finitely many isomorphism classes of abelian varieties with good reduction outside a fixed finite set of places, a result ultimately proved by Faltings.
• B. Weil conjectures
  The Weil conjectures are a set of deep statements about the zeta functions of algebraic varieties over finite fields that guided the development of modern algebraic geometry and were ultimately proved using étale cohomology.
• C. Standard Conjectures on Algebraic Cycles
  The Standard Conjectures on Algebraic Cycles are a set of deep, still unproven hypotheses in algebraic geometry that aim to provide a foundational theory of algebraic cycles and their cohomological properties, underpinning much of the modern theory of motives.
• D. Tate Conjecture
  The Tate Conjecture is a major open problem in arithmetic geometry that predicts a deep connection between algebraic cycles on varieties over finite fields and their Galois-invariant étale cohomology classes.
• E. Bombieri–Lang conjecture
  The Bombieri–Lang conjecture is a major unsolved conjecture in number theory and arithmetic geometry predicting that varieties of general type over number fields have only finitely many rational points.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Vojta’s conjectures
Target entity description: Vojta’s conjectures are a collection of deep conjectures in Diophantine geometry that generalize and unify results in number theory and Nevanlinna theory, with far-reaching implications including those related to the abc conjecture.

• A. Shafarevich conjecture for abelian varieties
  The Shafarevich conjecture for abelian varieties is a finiteness statement predicting that, over a number field, there are only finitely many isomorphism classes of abelian varieties with good reduction outside a fixed finite set of places, a result ultimately proved by Faltings.
• B. Weil conjectures
  The Weil conjectures are a set of deep statements about the zeta functions of algebraic varieties over finite fields that guided the development of modern algebraic geometry and were ultimately proved using étale cohomology.
• C. Standard Conjectures on Algebraic Cycles
  The Standard Conjectures on Algebraic Cycles are a set of deep, still unproven hypotheses in algebraic geometry that aim to provide a foundational theory of algebraic cycles and their cohomological properties, underpinning much of the modern theory of motives.
• D. Tate Conjecture
  The Tate Conjecture is a major open problem in arithmetic geometry that predicts a deep connection between algebraic cycles on varieties over finite fields and their Galois-invariant étale cohomology classes.
• E. Bombieri–Lang conjecture
  The Bombieri–Lang conjecture is a major unsolved conjecture in number theory and arithmetic geometry predicting that varieties of general type over number fields have only finitely many rational points.
• F. None of above. chosen