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: Kummer sequence | Statement: [Kummer theory, relatesTo, Kummer sequence]

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

• A. Kummer congruences
  Kummer congruences are number-theoretic relations describing how special values of Bernoulli numbers and related arithmetic functions behave modulo powers of primes, foundational in the study of p-adic L-functions and cyclotomic fields.
• B. 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.
• C. Bloch–Kato conjecture
  The Bloch–Kato conjecture is a deep statement in arithmetic geometry and K-theory that predicts an exact correspondence between Galois cohomology and Milnor K-theory, linking algebraic K-groups to field arithmetic.
• D. Gross–Koblitz formula
  The Gross–Koblitz formula is a result in number theory that expresses Gauss sums in terms of the p-adic gamma function, linking exponential sums over finite fields with p-adic analysis.
• E. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Kummer sequence
Target entity description: The Kummer sequence is a short exact sequence in algebraic number theory and algebraic geometry that relates a ring or scheme to its group of roots of unity and underpins Kummer theory and the study of cyclic extensions.

• A. Kummer congruences
  Kummer congruences are number-theoretic relations describing how special values of Bernoulli numbers and related arithmetic functions behave modulo powers of primes, foundational in the study of p-adic L-functions and cyclotomic fields.
• B. 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.
• C. Bloch–Kato conjecture
  The Bloch–Kato conjecture is a deep statement in arithmetic geometry and K-theory that predicts an exact correspondence between Galois cohomology and Milnor K-theory, linking algebraic K-groups to field arithmetic.
• D. Gross–Koblitz formula
  The Gross–Koblitz formula is a result in number theory that expresses Gauss sums in terms of the p-adic gamma function, linking exponential sums over finite fields with p-adic analysis.
• E. 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.
• F. None of above. chosen