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Oka coherence theorem (Theorem)

Let $M$ be a complex manifold.

Theorem 1   Suppose $\mathcal{F}$ is an analytic sheaf over $M$ that is a subsheaf of $\mathcal{O}^k$ If $\mathcal{F}$ is a locally finitely generated sheaf, then $\mathcal{F}$ is a coherent analytic sheaf.

Bibliography

1
Lars Hörmander. An Introduction to Complex Analysis in Several Variables, North-Holland Publishing Company, New York, New York, 1973.
2
Steven G. Krantz. Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, Rhode Island, 1992.




"Oka coherence theorem" is owned by jirka.
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Other names:  Oka theorem, Oka's theorem, Oka's coherence theorem
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Cross-references: coherent analytic sheaf, locally finitely generated sheaf, subsheaf, analytic sheaf, complex manifold
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This is version 2 of Oka coherence theorem, born on 2007-12-02, modified 2007-12-03.
Object id is 10085, canonical name is OkaCoherenceTheorem.
Accessed 1722 times total.

Classification:
AMS MSC32C35 (Several complex variables and analytic spaces :: Analytic spaces :: Analytic sheaves and cohomology groups)

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