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: p-adic numbers Q_p | Statement: [Hasse principle, completion, p-adic numbers Q_p]

Target entity: p-adic numbers Q_p
Context triple: [Hasse principle, completion, p-adic numbers Q_p]

• A. p-adic numbers chosen
  The p-adic numbers are a system of number fields that extend the rational numbers by measuring distance with respect to divisibility by a fixed prime p, playing a central role in modern number theory and arithmetic geometry.
• B. p-adic analytic groups
  p-adic analytic groups are topological groups over the p-adic numbers that locally resemble finite-dimensional p-adic manifolds and admit a compatible analytic structure.
• C. Gaussian rationals ℚ(i)
  Gaussian rationals ℚ(i) are the field of complex numbers whose real and imaginary parts are rational, formed by adjoining the imaginary unit i to the rational numbers.
• D. p-adic Hodge theory
  p-adic Hodge theory is a branch of arithmetic geometry that studies p-adic Galois representations and their relationship to the cohomology of algebraic varieties over p-adic fields, using analogues of classical Hodge-theoretic structures.
• E. Hasse–Arf theorem
  The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.