EGA III
E883475
EGA III is a foundational volume of Grothendieck and Dieudonné’s Éléments de Géométrie Algébrique that develops cohomology theory for schemes, including the formulation of Serre duality in the language of modern algebraic geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| EGA III canonical | 3 |
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
research monograph ⓘ volume of Éléments de Géométrie Algébrique ⓘ |
| aim | to provide a general cohomological framework for schemes ⓘ |
| author |
Alexander Grothendieck
NERFINISHED
ⓘ
Jean Dieudonné NERFINISHED ⓘ |
| contribution |
develops general base change theorems for cohomology
ⓘ
establishes general cohomology theory for proper morphisms of schemes ⓘ proves finiteness of higher direct images of coherent sheaves under proper morphisms ⓘ reformulates classical Serre duality using schemes and coherent sheaves ⓘ systematizes cohomological tools for algebraic geometry ⓘ |
| field | algebraic geometry ⓘ |
| follows | EGA II NERFINISHED ⓘ |
| framework | scheme theory ⓘ |
| hasCanonicalAbbreviation | EGA III NERFINISHED ⓘ |
| hasPart |
EGA III extsubscript{1}
ⓘ
EGA III extsubscript{2} ⓘ |
| influenced |
Grothendieck’s theory of schemes in SGA
ⓘ
development of duality theory in algebraic geometry ⓘ modern scheme-theoretic algebraic geometry ⓘ |
| inSeries | Publications Mathématiques de l’IHÉS NERFINISHED ⓘ |
| language | French ⓘ |
| mathematicalSubjectClassification |
14-XX
ⓘ
14Fxx ⓘ |
| originalTitle | Éléments de Géométrie Algébrique III NERFINISHED ⓘ |
| partOf | Éléments de Géométrie Algébrique NERFINISHED ⓘ |
| precedes | EGA IV NERFINISHED ⓘ |
| seriesNumber | III ⓘ |
| subjectOf | Serre duality in the language of schemes ⓘ |
| topic |
Grothendieck’s formalism of derived functors (at the level of δ-functors)
ⓘ
Serre duality NERFINISHED ⓘ base change in cohomology ⓘ coherent sheaf cohomology ⓘ cohomological dimension ⓘ cohomology of schemes ⓘ direct images of coherent sheaves ⓘ finiteness theorems ⓘ proper morphisms of schemes ⓘ |
| usesConcept |
Noetherian schemes
NERFINISHED
ⓘ
coherent sheaves ⓘ proper morphism ⓘ sheaf cohomology ⓘ |
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.