Weil group

Target entity: Weil group
Context triple: [André Weil, notableConcept, Weil group]

• A. Weyl group
  A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
• B. Hasse–Weil zeta function
  The Hasse–Weil zeta function is an analytic object in number theory that encodes arithmetic information about algebraic varieties over number fields, generalizing the Riemann zeta function and playing a central role in modern arithmetic geometry and conjectures like the Weil conjectures and the Birch–Swinnerton-Dyer conjecture.
• C. Kronecker–Weber theorem
  The Kronecker–Weber theorem is a fundamental result in algebraic number theory stating that every finite abelian extension of the rational numbers is contained in a cyclotomic field generated by roots of unity.
• D. Levine-Fricke Field
  Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
• 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. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Weil group
Target entity description: 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.

• A. Weyl group
  A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
• B. Hasse–Weil zeta function
  The Hasse–Weil zeta function is an analytic object in number theory that encodes arithmetic information about algebraic varieties over number fields, generalizing the Riemann zeta function and playing a central role in modern arithmetic geometry and conjectures like the Weil conjectures and the Birch–Swinnerton-Dyer conjecture.
• C. Kronecker–Weber theorem
  The Kronecker–Weber theorem is a fundamental result in algebraic number theory stating that every finite abelian extension of the rational numbers is contained in a cyclotomic field generated by roots of unity.
• D. Levine-Fricke Field
  Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
• 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. chosen