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: Hodge–Tate decomposition | Statement: [p-adic Hodge theory, studiesProperty, Hodge–Tate decomposition]

Target entity: Hodge–Tate decomposition
Context triple: [p-adic Hodge theory, studiesProperty, Hodge–Tate decomposition]

• A. Mazur's deformation theory of Galois representations
  Mazur's deformation theory of Galois representations is a foundational framework in number theory that systematically studies how p-adic Galois representations can be deformed, with deep applications to modular forms and the proof of Fermat’s Last Theorem.
• B. Weil–Deligne representations
  Weil–Deligne representations are algebraic objects combining a representation of the Weil group with a nilpotent operator, used to describe local Galois representations and formulate the local Langlands correspondence.
• C. 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.
• D. Serre’s conjecture on Galois representations
  Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
• 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. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Hodge–Tate decomposition
Target entity description: The Hodge–Tate decomposition is a fundamental result in p-adic Hodge theory that expresses p-adic Galois representations in terms of graded pieces analogous to Hodge structures, revealing how their arithmetic and geometric properties split into Tate-twisted components.

• A. Mazur's deformation theory of Galois representations
  Mazur's deformation theory of Galois representations is a foundational framework in number theory that systematically studies how p-adic Galois representations can be deformed, with deep applications to modular forms and the proof of Fermat’s Last Theorem.
• B. Weil–Deligne representations
  Weil–Deligne representations are algebraic objects combining a representation of the Weil group with a nilpotent operator, used to describe local Galois representations and formulate the local Langlands correspondence.
• C. p-adic Hodge theory chosen
  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.
• D. Serre’s conjecture on Galois representations
  Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
• 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.