Triple

T17647590
Position Surface form Disambiguated ID Type / Status
Subject David Eisenbud E429400 entity
Predicate notableWork P4 FINISHED
Object The Geometry of Schemes
The Geometry of Schemes is a graduate-level textbook by David Eisenbud and Joe Harris that provides an accessible, example-driven introduction to the language and techniques of scheme theory in modern algebraic geometry.
E1281445 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: The Geometry of Schemes | Statement: [David Eisenbud, notableWork, The Geometry of Schemes]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: The Geometry of Schemes
Context triple: [David Eisenbud, notableWork, The Geometry of Schemes]
  • 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. Serre’s cohomological methods in algebraic geometry
    Serre’s cohomological methods in algebraic geometry are foundational techniques that use sheaf cohomology to relate and study algebraic and analytic geometry, profoundly influencing modern algebraic geometry and complex geometry.
  • C. 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.
  • 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. 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.
  • 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: The Geometry of Schemes
Triple: [David Eisenbud, notableWork, The Geometry of Schemes]
Generated description
The Geometry of Schemes is a graduate-level textbook by David Eisenbud and Joe Harris that provides an accessible, example-driven introduction to the language and techniques of scheme theory in modern algebraic geometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: The Geometry of Schemes
Target entity description: The Geometry of Schemes is a graduate-level textbook by David Eisenbud and Joe Harris that provides an accessible, example-driven introduction to the language and techniques of scheme theory in modern 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. Serre’s cohomological methods in algebraic geometry
    Serre’s cohomological methods in algebraic geometry are foundational techniques that use sheaf cohomology to relate and study algebraic and analytic geometry, profoundly influencing modern algebraic geometry and complex geometry.
  • C. 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.
  • 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. 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.
  • 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_69d889e2c2608190b762e76d9b2262f1 completed April 10, 2026, 5:25 a.m.
NER Named-entity recognition batch_69e46e3a5ad8819085d4bef669fc3152 completed April 19, 2026, 5:55 a.m.
NED1 Entity disambiguation (via context triple) batch_6a021650aed4819089892c32c0236e3e completed May 11, 2026, 5:48 p.m.
NEDg Description generation batch_6a021a2ae13c8190a6a7a524b6c8879d completed May 11, 2026, 6:04 p.m.
NED2 Entity disambiguation (via description) batch_6a021ac1dd1c81909a1a13bc0556a985 completed May 11, 2026, 6:06 p.m.
Created at: April 10, 2026, 6:05 a.m.