Kummer pairing

Target entity: Kummer pairing
Context triple: [Kummer theory, relatesTo, Kummer pairing]

• A. Weil pairing
  The Weil pairing is a bilinear, alternating, non-degenerate pairing on the torsion points of an elliptic curve, fundamental in number theory and modern cryptography.
• B. Tate pairing
  The Tate pairing is a bilinear, non-degenerate pairing on the points of an elliptic curve (or abelian variety) over a finite field, fundamental in number theory and widely used in pairing-based cryptography.
• C. Cassels–Tate pairing
  The Cassels–Tate pairing is a bilinear pairing on the Tate–Shafarevich group of an abelian variety over a number field that plays a central role in arithmetic geometry and the study of rational points.
• D. Richelot isogeny
  The Richelot isogeny is a classical construction in algebraic geometry that gives a specific type of isogeny between principally polarized abelian surfaces, often described via genus-2 curves and their Jacobians.
• E. Kronecker pairing
  The Kronecker pairing is a fundamental bilinear map in algebraic topology that evaluates cohomology classes on homology classes, linking the two via an integer (or field) value.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Kummer pairing
Target entity description: Kummer pairing is a bilinear map in algebraic number theory that connects units or elements of a field with Galois cohomology, playing a central role in understanding abelian extensions via Kummer theory.

• A. Weil pairing
  The Weil pairing is a bilinear, alternating, non-degenerate pairing on the torsion points of an elliptic curve, fundamental in number theory and modern cryptography.
• B. Tate pairing
  The Tate pairing is a bilinear, non-degenerate pairing on the points of an elliptic curve (or abelian variety) over a finite field, fundamental in number theory and widely used in pairing-based cryptography.
• C. Cassels–Tate pairing
  The Cassels–Tate pairing is a bilinear pairing on the Tate–Shafarevich group of an abelian variety over a number field that plays a central role in arithmetic geometry and the study of rational points.
• D. Richelot isogeny
  The Richelot isogeny is a classical construction in algebraic geometry that gives a specific type of isogeny between principally polarized abelian surfaces, often described via genus-2 curves and their Jacobians.
• E. Kronecker pairing
  The Kronecker pairing is a fundamental bilinear map in algebraic topology that evaluates cohomology classes on homology classes, linking the two via an integer (or field) value.
• F. None of above. chosen