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.