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: global Artin map | Statement: [Artin reciprocity law, usesConcept, global Artin map]

Target entity: global Artin map
Context triple: [Artin reciprocity law, usesConcept, global Artin map]

• A. Artin L-functions
  Artin L-functions are complex analytic functions attached to Galois representations that generalize Dirichlet L-functions and play a central role in number theory and the study of arithmetic properties of fields.
• B. Artin reciprocity law
  The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
• C. Artin conductor
  The Artin conductor is an invariant in number theory that measures the ramification of Galois representations or characters of local and global fields, playing a key role in the study of L-functions and class field theory.
• D. Kummer map
  The Kummer map is a homomorphism in algebraic number theory and arithmetic geometry that connects elements of a field (or its units) to Galois cohomology classes, playing a key role in describing abelian extensions via Kummer theory.
• 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: global Artin map
Target entity description: The global Artin map is a central homomorphism in global class field theory that links idele or ideal class groups of a number field to its abelian Galois group, encoding the reciprocity laws governing abelian extensions.

• A. Artin L-functions
  Artin L-functions are complex analytic functions attached to Galois representations that generalize Dirichlet L-functions and play a central role in number theory and the study of arithmetic properties of fields.
• B. Artin reciprocity law chosen
  The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
• C. Artin conductor
  The Artin conductor is an invariant in number theory that measures the ramification of Galois representations or characters of local and global fields, playing a key role in the study of L-functions and class field theory.
• D. Kummer map
  The Kummer map is a homomorphism in algebraic number theory and arithmetic geometry that connects elements of a field (or its units) to Galois cohomology classes, playing a key role in describing abelian extensions via Kummer theory.
• 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.