# Oka coherence theorem

Let $M$ be a complex manifold^{}.

###### Theorem.

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

Title | Oka coherence theorem |
---|---|

Canonical name | OkaCoherenceTheorem |

Date of creation | 2013-03-22 17:39:08 |

Last modified on | 2013-03-22 17:39:08 |

Owner | jirka (4157) |

Last modified by | jirka (4157) |

Numerical id | 5 |

Author | jirka (4157) |

Entry type | Theorem |

Classification | msc 32C35 |

Synonym | Oka theorem |

Synonym | Oka’s theorem |

Synonym | Oka’s coherence theorem |