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: absolute Galois group of the rational numbers | Statement: [Galois representations, typicalDomain, absolute Galois group of the rational numbers]

Target entity: absolute Galois group of the rational numbers
Context triple: [Galois representations, typicalDomain, absolute Galois group of the rational numbers]

• A. Chebotarev density theorem
  The Chebotarev density theorem is a fundamental result in algebraic number theory that generalizes the prime number theorem to describe how often primes in a number field have a given Frobenius conjugacy class in its Galois group.
• B. Galois representations
  Galois representations are homomorphisms from Galois groups of field extensions into matrix groups that encode deep arithmetic information and link number theory with algebraic geometry and modular forms.
• C. cosmic Galois group
  The cosmic Galois group is a conjectural symmetry group acting on periods and structures arising in quantum field theory and arithmetic geometry, proposed to unify and explain deep relations between Feynman integrals, motives, and number-theoretic phenomena.
• D. Serre’s conjecture on Galois representations
  Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
• E. Artin’s conjecture on L-functions
  Artin’s conjecture on L-functions is a major unproven hypothesis in number theory asserting that nontrivial Artin L-functions associated to Galois representations are entire, with deep implications for the distribution of primes and the structure of number fields.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: absolute Galois group of the rational numbers
Target entity description: The absolute Galois group of the rational numbers is the profinite group of all field automorphisms of an algebraic closure of Q that fix Q, encoding the full arithmetic and algebraic extension structure of the rational numbers.

• A. Chebotarev density theorem
  The Chebotarev density theorem is a fundamental result in algebraic number theory that generalizes the prime number theorem to describe how often primes in a number field have a given Frobenius conjugacy class in its Galois group.
• B. Galois representations
  Galois representations are homomorphisms from Galois groups of field extensions into matrix groups that encode deep arithmetic information and link number theory with algebraic geometry and modular forms.
• C. cosmic Galois group
  The cosmic Galois group is a conjectural symmetry group acting on periods and structures arising in quantum field theory and arithmetic geometry, proposed to unify and explain deep relations between Feynman integrals, motives, and number-theoretic phenomena.
• D. Serre’s conjecture on Galois representations
  Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
• E. Artin’s conjecture on L-functions
  Artin’s conjecture on L-functions is a major unproven hypothesis in number theory asserting that nontrivial Artin L-functions associated to Galois representations are entire, with deep implications for the distribution of primes and the structure of number fields.
• F. None of above. chosen