Triple

T10772698
Position Surface form Disambiguated ID Type / Status
Subject Grothendieck–Riemann–Roch theorem E254119 entity
Predicate appearsIn P795 FINISHED
Object FGA (Fondements de la géométrie algébrique)
FGA (Fondements de la géométrie algébrique) is a foundational collection of Alexander Grothendieck’s seminar expositions that systematically developed modern algebraic geometry, including major results such as the Grothendieck–Riemann–Roch theorem.
E886802 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: FGA (Fondements de la géométrie algébrique) | Statement: [Grothendieck–Riemann–Roch theorem, appearsIn, FGA (Fondements de la géométrie algébrique)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: FGA (Fondements de la géométrie algébrique)
Context triple: [Grothendieck–Riemann–Roch theorem, appearsIn, FGA (Fondements de la géométrie algébrique)]
  • A. GAGA (Géométrie Algébrique et Géométrie Analytique)
    GAGA (Géométrie Algébrique et Géométrie Analytique) is Jean-Pierre Serre’s foundational 1956 paper establishing deep equivalences between algebraic geometry and complex analytic geometry, particularly for projective varieties.
  • B. Éléments de géométrie algébrique
    Éléments de géométrie algébrique is a foundational multi-volume treatise that reshaped modern algebraic geometry by developing the theory of schemes and cohomology in a highly general, abstract framework.
  • C. Séminaire de Géométrie Algébrique du Bois Marie
    Séminaire de Géométrie Algébrique du Bois Marie is a foundational multi-volume series of advanced seminars that reshaped modern algebraic geometry through the development of schemes, cohomology theories, and the Grothendieck school’s methods.
  • D. L’Analysis Situs et la Géométrie Algébrique
    L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
  • E. Théorie des intersections et théorème de Riemann–Roch
    "Théorie des intersections et théorème de Riemann–Roch" is a volume of the Séminaire de Géométrie Algébrique (SGA 6) that develops the foundations of intersection theory in algebraic geometry and establishes a general form of the Riemann–Roch theorem.
  • 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: FGA (Fondements de la géométrie algébrique)
Triple: [Grothendieck–Riemann–Roch theorem, appearsIn, FGA (Fondements de la géométrie algébrique)]
Generated description
FGA (Fondements de la géométrie algébrique) is a foundational collection of Alexander Grothendieck’s seminar expositions that systematically developed modern algebraic geometry, including major results such as the Grothendieck–Riemann–Roch theorem.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: FGA (Fondements de la géométrie algébrique)
Target entity description: FGA (Fondements de la géométrie algébrique) is a foundational collection of Alexander Grothendieck’s seminar expositions that systematically developed modern algebraic geometry, including major results such as the Grothendieck–Riemann–Roch theorem.
  • A. GAGA (Géométrie Algébrique et Géométrie Analytique)
    GAGA (Géométrie Algébrique et Géométrie Analytique) is Jean-Pierre Serre’s foundational 1956 paper establishing deep equivalences between algebraic geometry and complex analytic geometry, particularly for projective varieties.
  • B. Éléments de géométrie algébrique
    Éléments de géométrie algébrique is a foundational multi-volume treatise that reshaped modern algebraic geometry by developing the theory of schemes and cohomology in a highly general, abstract framework.
  • C. Séminaire de Géométrie Algébrique du Bois Marie
    Séminaire de Géométrie Algébrique du Bois Marie is a foundational multi-volume series of advanced seminars that reshaped modern algebraic geometry through the development of schemes, cohomology theories, and the Grothendieck school’s methods.
  • D. L’Analysis Situs et la Géométrie Algébrique
    L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
  • E. Théorie des intersections et théorème de Riemann–Roch
    "Théorie des intersections et théorème de Riemann–Roch" is a volume of the Séminaire de Géométrie Algébrique (SGA 6) that develops the foundations of intersection theory in algebraic geometry and establishes a general form of the Riemann–Roch theorem.
  • 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_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_69de84b88ba08190afddea2976d12465 completed April 14, 2026, 6:17 p.m.
NEDg Description generation batch_69de883488b481909f151d8a7c246aa1 completed April 14, 2026, 6:32 p.m.
NED2 Entity disambiguation (via description) batch_69de8e80fe80819088ac76bb5abc58f0 completed April 14, 2026, 6:59 p.m.
Created at: April 8, 2026, 9:16 p.m.