Derived Algebraic Geometry (series of papers)
E1266020
UNEXPLORED
Derived Algebraic Geometry is Jacob Lurie’s influential series of papers that develops a modern, higher-categorical foundation for algebraic geometry using derived and homotopical methods.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Derived Algebraic Geometry (series of papers) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T17386424 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Derived Algebraic Geometry (series of papers) Context triple: [Jacob Lurie, notableWork, Derived Algebraic Geometry (series of papers)]
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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.
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B.
Gabriel localization theory
Gabriel localization theory is a framework in homological algebra and category theory that studies how to construct and analyze localizations of Grothendieck categories via torsion theories and exact functors.
-
C.
Grothendieck duality
Grothendieck duality is a foundational theory in algebraic geometry that generalizes classical Serre duality to a broad categorical and sheaf-theoretic framework for studying duality on schemes and morphisms.
-
D.
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.
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E.
Grothendieck toposes
Grothendieck toposes are highly structured categories that generalize topological spaces and serve as a unifying framework for geometry, logic, and cohomology in modern mathematics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Derived Algebraic Geometry (series of papers) Target entity description: Derived Algebraic Geometry is Jacob Lurie’s influential series of papers that develops a modern, higher-categorical foundation for algebraic geometry using derived and homotopical methods.
-
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.
Gabriel localization theory
Gabriel localization theory is a framework in homological algebra and category theory that studies how to construct and analyze localizations of Grothendieck categories via torsion theories and exact functors.
-
C.
Grothendieck duality
Grothendieck duality is a foundational theory in algebraic geometry that generalizes classical Serre duality to a broad categorical and sheaf-theoretic framework for studying duality on schemes and morphisms.
-
D.
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.
-
E.
Grothendieck toposes
Grothendieck toposes are highly structured categories that generalize topological spaces and serve as a unifying framework for geometry, logic, and cohomology in modern mathematics.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.