Triple
T10732801
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Serre duality |
E253115
|
entity |
| Predicate | isSpecialCaseOf |
P2372
|
FINISHED |
| Object | Grothendieck–Verdier duality |
E254134
|
NE FINISHED |
How this triple was built (2 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: Grothendieck–Verdier duality | Statement: [Serre duality, isSpecialCaseOf, Grothendieck–Verdier duality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Grothendieck–Verdier duality Context triple: [Serre duality, isSpecialCaseOf, Grothendieck–Verdier duality]
-
A.
Grothendieck duality
chosen
Grothendieck duality is a foundational theory in algebraic geometry that generalizes classical Serre duality to a broad categorical and sheaf-theoretic framework for studying duality on schemes and morphisms.
-
B.
Verdier duality
Verdier duality is a powerful generalization of Poincaré duality formulated in the language of derived categories and sheaf theory, providing a duality functor that relates cohomology with compact support to ordinary cohomology on possibly singular or non-compact spaces.
-
C.
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.
-
D.
Théorie des topos et cohomologie étale des schémas
Théorie des topos et cohomologie étale des schémas is a foundational multi-volume work in algebraic geometry, originating from Grothendieck’s Séminaire de Géométrie Algébrique, that develops topos theory and étale cohomology of schemes.
-
E.
Gabriel localization theory
Gabriel localization theory is a framework in homological algebra and category theory that studies how to construct and analyze localizations of Grothendieck categories via torsion theories and exact functors.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69de557c4ea4819090b0c6c2175e05ea |
completed | April 14, 2026, 2:55 p.m. |
Created at: April 8, 2026, 9:14 p.m.