GAGA
E883477
GAGA (Géométrie Algébrique et Géométrie Analytique) is a foundational theory in mathematics, developed by Jean-Pierre Serre, that establishes deep connections between algebraic geometry and complex analytic geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| GAGA canonical | 1 |
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
equivalence theorem
ⓘ
mathematical theory ⓘ |
| acronymFor | Géométrie Algébrique et Géométrie Analytique NERFINISHED ⓘ |
| appliesTo |
complex projective varieties
ⓘ
proper algebraic varieties over the complex numbers ⓘ |
| area |
complex algebraic geometry
ⓘ
complex analytic geometry ⓘ |
| author | Jean-Pierre Serre NERFINISHED ⓘ |
| baseField | complex numbers ⓘ |
| canonicalReference | Serre, J.-P., "Géométrie Algébrique et Géométrie Analytique (GAGA)", Publ. Math. IHÉS 4 (1956) NERFINISHED ⓘ |
| comparisonType |
equivalence of categories
ⓘ
isomorphism of cohomology groups ⓘ |
| context | theory of schemes (precursor setting) ⓘ |
| developer | Jean-Pierre Serre NERFINISHED ⓘ |
| establishesConnectionBetween |
algebraic geometry
ⓘ
complex analytic geometry ⓘ |
| field |
algebraic geometry
ⓘ
complex analytic geometry ⓘ |
| fullName | Géométrie Algébrique et Géométrie Analytique NERFINISHED ⓘ |
| hasImpactOn |
Hodge theory
ⓘ
algebraization problems in geometry ⓘ moduli theory ⓘ |
| hasResult |
algebraization of analytic objects under properness hypotheses
ⓘ
equivalence between algebraic and analytic coherent sheaves on projective varieties ⓘ isomorphism between algebraic and analytic cohomology groups for coherent sheaves ⓘ |
| historicalImportance | foundational link between algebraic and analytic geometry ⓘ |
| influenced |
comparison theorems in arithmetic geometry
ⓘ
modern algebraic geometry ⓘ theory of schemes ⓘ |
| language | French ⓘ |
| mainTheme | comparison between algebraic and analytic categories ⓘ |
| namedAfter | initial letters of Géométrie Algébrique et Géométrie Analytique ⓘ |
| provides |
comparison theorems for cohomology
ⓘ
criteria for algebraicity of analytic objects ⓘ equivalence of coherent sheaf categories in projective case ⓘ |
| publicationYear | 1956 ⓘ |
| publishedIn | Publications Mathématiques de l’IHÉS NERFINISHED ⓘ |
| relatedTo |
Cartan–Serre theory of coherent analytic sheaves
NERFINISHED
ⓘ
Serre’s finiteness theorems NERFINISHED ⓘ |
| relates |
compact complex analytic spaces
ⓘ
projective algebraic varieties ⓘ |
| typicalAssumption |
finite type over the complex numbers
ⓘ
properness of the algebraic variety ⓘ |
| usesConcept |
analytic continuation
ⓘ
coherent sheaf ⓘ sheaf cohomology ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.