Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Stein_manifolds
coherent analytic sheaves |
| gptkbp:field |
complex geometry
sheaf theory complex analytic geometry |
| https://www.w3.org/2000/01/rdf-schema#label |
Cartan's Theorems A and B
|
| gptkbp:importantFor |
basis for modern complex geometry
fundamental results in the theory of analytic sheaves |
| gptkbp:influenced |
gptkb:algebraic_geometry
gptkb:Oka's_coherence_theorem gptkb:Serre's_GAGA_principle |
| gptkbp:namedAfter |
gptkb:Henri_Cartan
|
| gptkbp:publishedIn |
gptkb:Annales_Scientifiques_de_l'École_Normale_Supérieure
|
| gptkbp:theoremAStatement |
Every coherent analytic sheaf on a Stein manifold is generated by its global sections.
|
| gptkbp:theoremBStatement |
The higher cohomology groups of a coherent analytic sheaf on a Stein manifold vanish.
|
| gptkbp:year |
1953
|
| gptkbp:bfsParent |
gptkb:Stein_manifold
|
| gptkbp:bfsLayer |
7
|