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: Lefschetz decomposition of cohomology | Statement: [Hard Lefschetz theorem, implies, Lefschetz decomposition of cohomology]

Target entity: Lefschetz decomposition of cohomology
Context triple: [Hard Lefschetz theorem, implies, Lefschetz decomposition of cohomology]

• A. Lefschetz decomposition chosen
  Lefschetz decomposition is a structural breakdown of the derived category of coherent sheaves on an algebraic variety into a sequence of subcategories reflecting the geometry of a Lefschetz-type fibration or embedding.
• B. Hodge decomposition
  Hodge decomposition is a fundamental result in differential geometry and Hodge theory that expresses differential forms on a Riemannian manifold uniquely as sums of exact, co-exact, and harmonic components.
• C. Hard Lefschetz theorem
  The Hard Lefschetz theorem is a fundamental result in algebraic geometry and Hodge theory that relates the cohomology groups of a compact Kähler manifold via repeated cup product with the Kähler class, yielding powerful symmetry and duality properties.
• D. Dolbeault cohomology classes
  Dolbeault cohomology classes are equivalence classes of differential forms on a complex manifold defined using the ∂̄-operator, encoding the manifold’s complex-analytic and geometric structure.
• E. Deligne cohomology
  Deligne cohomology is a refined cohomology theory in algebraic geometry that combines singular cohomology and differential forms to capture both topological and arithmetic information about complex algebraic varieties.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.