Triple
T10772990
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Éléments de géométrie algébrique |
E254127
|
entity |
| Predicate | influenced |
P9
|
FINISHED |
| Object |
Grothendieck school of algebraic geometry
The Grothendieck school of algebraic geometry is a mid-20th-century mathematical movement led by Alexander Grothendieck that revolutionized algebraic geometry through the development of schemes, sheaf theory, and cohomological methods.
|
E627992
|
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: Grothendieck school of algebraic geometry | Statement: [Éléments de géométrie algébrique, influenced, Grothendieck school of algebraic geometry]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Grothendieck school of algebraic geometry Context triple: [Éléments de géométrie algébrique, influenced, Grothendieck school of algebraic geometry]
-
A.
Grothendieck’s scheme-theoretic framework
Grothendieck’s scheme-theoretic framework is a foundational reformulation of algebraic geometry that generalizes varieties using schemes, enabling powerful tools like sheaf theory, cohomology, and modern number-theoretic applications.
-
B.
Foundations of Algebraic Geometry
Foundations of Algebraic Geometry is a landmark mathematical treatise that systematically developed the modern foundations of algebraic geometry and profoundly influenced the field’s subsequent evolution.
-
C.
Bourbaki school of mathematics
The Bourbaki school of mathematics is a collective pseudonymous group of mainly French mathematicians known for their rigorous, abstract, and axiomatic reformulation of modern mathematics through influential multi-volume treatises.
-
D.
Grothendieck topology
A Grothendieck topology is an abstract framework in category theory that generalizes the notion of open covers in topology to define sheaves on arbitrary categories.
-
E.
Topological Methods in Algebraic Geometry
Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
- 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: Grothendieck school of algebraic geometry Triple: [Éléments de géométrie algébrique, influenced, Grothendieck school of algebraic geometry]
Generated description
The Grothendieck school of algebraic geometry is a mid-20th-century mathematical movement led by Alexander Grothendieck that revolutionized algebraic geometry through the development of schemes, sheaf theory, and cohomological methods.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Grothendieck school of algebraic geometry Target entity description: The Grothendieck school of algebraic geometry is a mid-20th-century mathematical movement led by Alexander Grothendieck that revolutionized algebraic geometry through the development of schemes, sheaf theory, and cohomological methods.
-
A.
Grothendieck’s scheme-theoretic framework
chosen
Grothendieck’s scheme-theoretic framework is a foundational reformulation of algebraic geometry that generalizes varieties using schemes, enabling powerful tools like sheaf theory, cohomology, and modern number-theoretic applications.
-
B.
Foundations of Algebraic Geometry
Foundations of Algebraic Geometry is a landmark mathematical treatise that systematically developed the modern foundations of algebraic geometry and profoundly influenced the field’s subsequent evolution.
-
C.
Bourbaki school of mathematics
The Bourbaki school of mathematics is a collective pseudonymous group of mainly French mathematicians known for their rigorous, abstract, and axiomatic reformulation of modern mathematics through influential multi-volume treatises.
-
D.
Grothendieck topology
A Grothendieck topology is an abstract framework in category theory that generalizes the notion of open covers in topology to define sheaves on arbitrary categories.
-
E.
Topological Methods in Algebraic Geometry
Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
- F. None of above.
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_69d6aa5f54f4819082d0bbcb6f8797e6 |
completed | April 8, 2026, 7:19 p.m. |
| NER | Named-entity recognition | batch_69d7329b27748190bd0e2569c7972fd1 |
completed | April 9, 2026, 5:01 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69de238559b48190abc759e744ab0f8e |
completed | April 14, 2026, 11:22 a.m. |
| NEDg | Description generation | batch_69de271fb08c8190a44c547083226fd8 |
completed | April 14, 2026, 11:38 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69de2cecc24c8190a240366e0600426a |
completed | April 14, 2026, 12:02 p.m. |
Created at: April 8, 2026, 9:16 p.m.