Triple

T10772798
Position Surface form Disambiguated ID Type / Status
Subject SGA 6 E254121 entity
Predicate title P38 FINISHED
Object 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.
E886195 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: Théorie des intersections et théorème de Riemann–Roch | Statement: [SGA 6, title, Théorie des intersections et théorème de Riemann–Roch]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Théorie des intersections et théorème de Riemann–Roch
Context triple: [SGA 6, title, Théorie des intersections et théorème de Riemann–Roch]
  • A. 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.
  • B. Sur les courbes algébriques et les variétés qui s’en déduisent
    Sur les courbes algébriques et les variétés qui s’en déduisent is a foundational 1948 monograph by André Weil that helped establish modern algebraic geometry and introduced key ideas leading to the Weil conjectures.
  • C. 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.
  • 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. Grothendieck–Ogg–Shafarevich formula
    The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
  • 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: Théorie des intersections et théorème de Riemann–Roch
Triple: [SGA 6, title, Théorie des intersections et théorème de Riemann–Roch]
Generated description
"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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Théorie des intersections et théorème de Riemann–Roch
Target entity description: "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.
  • A. 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.
  • B. Sur les courbes algébriques et les variétés qui s’en déduisent
    Sur les courbes algébriques et les variétés qui s’en déduisent is a foundational 1948 monograph by André Weil that helped establish modern algebraic geometry and introduced key ideas leading to the Weil conjectures.
  • C. 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.
  • 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. Grothendieck–Ogg–Shafarevich formula
    The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
  • 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_69de55daf52c8190aee3bca39cdc5d55 completed April 14, 2026, 2:57 p.m.
NEDg Description generation batch_69de5eacae148190b7ca2da87427572e completed April 14, 2026, 3:35 p.m.
NED2 Entity disambiguation (via description) batch_69de6397ff688190b6788489895a5360 completed April 14, 2026, 3:56 p.m.
Created at: April 8, 2026, 9:16 p.m.