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.