Triple

T10732942
Position Surface form Disambiguated ID Type / Status
Subject Cohomologie Galoisienne E253118 entity
Predicate topic P261 FINISHED
Object Poitou–Tate duality
Poitou–Tate duality is a fundamental result in Galois cohomology that establishes deep duality relationships between global and local cohomology groups of number fields.
E883485 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
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).
Input
Phrase: Poitou–Tate duality | Statement: [Cohomologie Galoisienne, topic, Poitou–Tate duality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Poitou–Tate duality
Context triple: [Cohomologie Galoisienne, topic, Poitou–Tate duality]
  • A. Cassels–Tate pairing
    The Cassels–Tate pairing is a bilinear pairing on the Tate–Shafarevich group of an abelian variety over a number field that plays a central role in arithmetic geometry and the study of rational points.
  • B. Tate Conjecture
    The Tate Conjecture is a major open problem in arithmetic geometry that predicts a deep connection between algebraic cycles on varieties over finite fields and their Galois-invariant étale cohomology classes.
  • C. Sato–Tate distribution (for families of elliptic curves)
    The Sato–Tate distribution (for families of elliptic curves) is a probabilistic law describing how the normalized Frobenius traces (or equivalently, the angles in the Hasse bound) of elliptic curves are distributed, typically following a specific sine-squared measure on the interval [0, π].
  • D. Pontryagin duality
    Pontryagin duality is a fundamental theorem in harmonic analysis and topological group theory that establishes a duality between locally compact abelian groups and their groups of continuous characters.
  • E. Deligne–Lusztig theory
    Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Poitou–Tate duality
Triple: [Cohomologie Galoisienne, topic, Poitou–Tate duality]
Generated description
Poitou–Tate duality is a fundamental result in Galois cohomology that establishes deep duality relationships between global and local cohomology groups of number fields.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Poitou–Tate duality
Target entity description: Poitou–Tate duality is a fundamental result in Galois cohomology that establishes deep duality relationships between global and local cohomology groups of number fields.
  • A. Cassels–Tate pairing
    The Cassels–Tate pairing is a bilinear pairing on the Tate–Shafarevich group of an abelian variety over a number field that plays a central role in arithmetic geometry and the study of rational points.
  • B. Tate Conjecture
    The Tate Conjecture is a major open problem in arithmetic geometry that predicts a deep connection between algebraic cycles on varieties over finite fields and their Galois-invariant étale cohomology classes.
  • C. Sato–Tate distribution (for families of elliptic curves)
    The Sato–Tate distribution (for families of elliptic curves) is a probabilistic law describing how the normalized Frobenius traces (or equivalently, the angles in the Hasse bound) of elliptic curves are distributed, typically following a specific sine-squared measure on the interval [0, π].
  • D. Pontryagin duality
    Pontryagin duality is a fundamental theorem in harmonic analysis and topological group theory that establishes a duality between locally compact abelian groups and their groups of continuous characters.
  • E. Deligne–Lusztig theory
    Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d6aa5d8be481909a43218b2bfdbe95 completed April 8, 2026, 7:19 p.m.
NER Named-entity recognition batch_69d7101ff9808190a27fcc06da097ea3 completed April 9, 2026, 2:34 a.m.
NED1 Entity disambiguation (via context triple) batch_69de22bb62e481909544c87801012df3 completed April 14, 2026, 11:19 a.m.
NEDg Description generation batch_69de271ca4f081908d78a20b25ebd25c completed April 14, 2026, 11:38 a.m.
NED2 Entity disambiguation (via description) batch_69de2ccee0cc8190acd24d5c225f7cde completed April 14, 2026, 12:02 p.m.
Created at: April 8, 2026, 9:14 p.m.