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 theorems | Statement: [Hard Lefschetz theorem, isPartOf, Lefschetz theorems]

Target entity: Lefschetz theorems
Context triple: [Hard Lefschetz theorem, isPartOf, Lefschetz theorems]

• A. Lefschetz hyperplane theorem
  The Lefschetz hyperplane theorem is a fundamental result in algebraic geometry and topology that relates the topology (especially homology and homotopy groups) of a smooth projective variety to that of its hyperplane sections.
• B. Grothendieck–Lefschetz theorem
  The Grothendieck–Lefschetz theorem is a fundamental result in algebraic geometry that extends Lefschetz-type hyperplane theorems to a broad scheme-theoretic and cohomological setting, relating the geometry and Picard groups of a variety to those of its hyperplane sections.
• C. Hard Lefschetz theorem chosen
  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. Chevalley’s theorem in algebraic geometry
  Chevalley’s theorem in algebraic geometry is a fundamental result stating that the image of a morphism of finite type between schemes (or varieties) is a constructible set, playing a key role in understanding how geometric properties behave under mappings.
• E. Grothendieck–Riemann–Roch theorem
  The Grothendieck–Riemann–Roch theorem is a fundamental result in algebraic geometry that generalizes the classical Riemann–Roch theorem by relating pushforwards in K-theory to pushforwards in cohomology via characteristic classes.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.