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: Artin–Tate: Class Field Theory | Statement: [global class field theory, typicalReference, Artin–Tate: Class Field Theory]

Target entity: Artin–Tate: Class Field Theory
Context triple: [global class field theory, typicalReference, Artin–Tate: Class Field Theory]

• A. Furtwängler’s theorem in class field theory
  Furtwängler’s theorem in class field theory is a fundamental result in algebraic number theory that refines the principal ideal theorem by describing how ideal classes capitulate (become principal) in certain abelian extensions of number fields.
• B. Cassels–Fröhlich: Algebraic Number Theory
  Cassels–Fröhlich: Algebraic Number Theory is a classic graduate-level textbook that provides a comprehensive and rigorous introduction to algebraic number theory and its foundational results.
• C. Algebraic Groups and Class Fields
  "Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
• D. Neukirch: Algebraic Number Theory
  "Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
• E. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Artin–Tate: Class Field Theory
Target entity description: Artin–Tate: Class Field Theory is a classic textbook that provides a rigorous and accessible introduction to global and local class field theory in algebraic number theory.

• A. Furtwängler’s theorem in class field theory
  Furtwängler’s theorem in class field theory is a fundamental result in algebraic number theory that refines the principal ideal theorem by describing how ideal classes capitulate (become principal) in certain abelian extensions of number fields.
• B. Cassels–Fröhlich: Algebraic Number Theory
  Cassels–Fröhlich: Algebraic Number Theory is a classic graduate-level textbook that provides a comprehensive and rigorous introduction to algebraic number theory and its foundational results.
• C. Algebraic Groups and Class Fields
  "Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
• D. Neukirch: Algebraic Number Theory
  "Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
• E. 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.
• F. None of above. chosen

Target predicate: typicalReference
Context triple: [global class field theory, typicalReference, Artin–Tate: Class Field Theory]

• A. typicalIn
  Indicates that something commonly occurs, appears, or is found within a given context, category, or environment.
• B. standardReference chosen
  Indicates that one entity serves as the authoritative or canonical reference or benchmark for interpreting, validating, or comparing another entity.
• C. typicalBase
  Indicates that one entity serves as the standard or most representative base or foundation for another entity in typical or common cases.
• D. referenceType
  Indicates the specific kind or category of reference relationship that one entity has to another.
• E. typicalCoreType
  Indicates that something is a standard or characteristic core type within a given classification or system.
• F. None of above.