# Oka coherence theorem

Let $M$ be a complex manifold.

###### Theorem.

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.

## References

• 1 Lars Hörmander. , North-Holland Publishing Company, New York, New York, 1973.
• 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
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