GAGA (Géométrie Algébrique et Géométrie Analytique)

E253117

GAGA (Géométrie Algébrique et Géométrie Analytique) is Jean-Pierre Serre’s foundational 1956 paper establishing deep equivalences between algebraic geometry and complex analytic geometry, particularly for projective varieties.

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Statements (44)

Predicate Object
instanceOf foundational work in algebraic geometry ⓘ
mathematical research paper ⓘ
abbreviation GAGA ⓘ
associatedWith GAGA theorems ⓘ
Serre’s cohomological methods in algebraic geometry ⓘ
author Jean-Pierre Serre ⓘ
citationStyle commonly cited simply as “GAGA” in mathematical literature ⓘ
context varieties over the field of complex numbers ⓘ
establishes comparison theorems between algebraic and analytic cohomology ⓘ
equivalence between algebraic and analytic Picard groups for projective complex varieties ⓘ
equivalence of categories between coherent algebraic sheaves and coherent analytic sheaves on complex projective varieties ⓘ
finiteness results for cohomology of coherent sheaves on projective varieties ⓘ
field algebraic geometry ⓘ
complex analytic geometry ⓘ
focusesOn projective varieties ⓘ
historicalSignificance key step in the transition from classical to modern algebraic geometry ⓘ
one of the earliest systematic uses of sheaf cohomology in algebraic geometry ⓘ
impact bridged algebraic geometry and complex analytic geometry ⓘ
influenced the development of scheme-theoretic algebraic geometry ⓘ
provided foundations for modern comparison theorems in geometry ⓘ
influenced Grothendieck’s formulation of comparison theorems for schemes ⓘ
later generalizations of GAGA to non-projective and non-compact settings ⓘ
influencedBy Cartan–Serre theory of coherent analytic sheaves ⓘ
introducesConcept GAGA principle ⓘ
language French ⓘ
mainTheme equivalence between algebraic and analytic geometry ⓘ
mathematicsSubjectClassification 14-XX algebraic geometry ⓘ
32-XX several complex variables and analytic spaces ⓘ
publicationYear 1956 ⓘ
publishedIn Annales de l’Institut Fourier ⓘ
relatedConcept Serre’s finiteness theorem ⓘ
Serre’s theorem on projective embeddings via ample line bundles ⓘ
shows analytic global sections of coherent sheaves on projective varieties are algebraic ⓘ
equivalence between algebraic and analytic morphisms for projective varieties over the complex numbers ⓘ
every analytic coherent sheaf on a complex projective variety is algebraizable ⓘ
holomorphic line bundles on complex projective varieties come from algebraic line bundles ⓘ
title Géométrie Algébrique et Géométrie Analytique ⓘ
topic coherent sheaves on projective varieties ⓘ
comparison of algebraic and analytic cohomology groups ⓘ
comparison of algebraic and analytic line bundles ⓘ
comparison of algebraic and analytic vector bundles ⓘ
properness and projectivity in the analytic and algebraic categories ⓘ
usesTool cohomology of sheaves ⓘ
sheaf theory ⓘ

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Referenced by (7)

Full triples — surface form annotated when it differs from this entity's canonical label.

Jean-Pierre Serre → notableWork → GAGA (Géométrie Algébrique et Géométrie Analytique) ⓘ
GAGA (Géométrie Algébrique et Géométrie Analytique) → title → Géométrie Algébrique et Géométrie Analytique ⓘ
linked to: GAGA (Géométrie Algébrique et Géométrie Analytique)
GAGA → fullName → Géométrie Algébrique et Géométrie Analytique ⓘ
linked to: GAGA (Géométrie Algébrique et Géométrie Analytique)
GAGA → acronymFor → Géométrie Algébrique et Géométrie Analytique ⓘ
linked to: GAGA (Géométrie Algébrique et Géométrie Analytique)
GAGA → canonicalReference → Serre, J.-P., "Géométrie Algébrique et Géométrie Analytique (GAGA)", Publ. Math. IHÉS 4 (1956) ⓘ
linked to: GAGA (Géométrie Algébrique et Géométrie Analytique)
GAGA principle → statedIn → Géométrie Algébrique et Géométrie Analytique ⓘ
linked to: GAGA (Géométrie Algébrique et Géométrie Analytique)
GAGA principle → abbreviationFor → Géométrie Algébrique et Géométrie Analytique ⓘ
linked to: GAGA (Géométrie Algébrique et Géométrie Analytique)