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: Hilbert class field theory | Statement: [global class field theory, generalizes, Hilbert class field theory]

Target entity: Hilbert class field theory
Context triple: [global class field theory, generalizes, Hilbert class field theory]

• A. Hilbert class field chosen
  The Hilbert class field of a number field is its maximal unramified abelian extension, central in class field theory as it corresponds to the field’s ideal class group.
• B. 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.
• C. Iwasawa theory
  Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
• D. Kummer theory
  Kummer theory is a branch of algebraic number theory that studies abelian extensions of fields, especially cyclotomic and radical extensions, using properties of roots of unity and ideal class groups.
• E. Hilbert’s twelfth problem
  Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.