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: idèle class group | Statement: [Weil group, relatedTo, idèle class group]

Target entity: idèle class group
Context triple: [Weil group, relatedTo, idèle class group]

• A. Hilbert class field
  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. Dedekind ideal
  A Dedekind ideal is a type of ideal in ring theory central to algebraic number theory, particularly in the study of Dedekind domains and unique factorization of ideals.
• C. Weil group
  The Weil group is an extension of the absolute Galois group introduced by André Weil to refine class field theory and play a central role in the formulation of the local and global Langlands correspondences.
• D. 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.
• E. Brauer group
  The Brauer group is an algebraic structure that classifies equivalence classes of central simple algebras over a field (or more general schemes), playing a key role in number theory, algebraic geometry, and cohomology.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: idèle class group
Triple: [Weil group, relatedTo, idèle class group]

The idèle class group is a fundamental arithmetic object in number theory that encodes global information about a number field via its idèles and plays a central role in class field theory.

Target entity: idèle class group
Target entity description: The idèle class group is a fundamental arithmetic object in number theory that encodes global information about a number field via its idèles and plays a central role in class field theory.

• A. Hilbert class field
  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. Dedekind ideal
  A Dedekind ideal is a type of ideal in ring theory central to algebraic number theory, particularly in the study of Dedekind domains and unique factorization of ideals.
• C. Weil group
  The Weil group is an extension of the absolute Galois group introduced by André Weil to refine class field theory and play a central role in the formulation of the local and global Langlands correspondences.
• D. 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.
• E. Brauer group
  The Brauer group is an algebraic structure that classifies equivalence classes of central simple algebras over a field (or more general schemes), playing a key role in number theory, algebraic geometry, and cohomology.
• F. None of above. chosen