# Cartan theorem B

###### Theorem (Cartan).

Suppose $\mathrm{F}$ is a coherent analytic sheaf on a Stein manifold $M$. Then for $k\mathrm{>}\mathrm{0}$, then

$${H}^{k}(M,\mathcal{F})=0.$$ |

Here, ${H}^{k}(M,\mathcal{F})$ is the $k$th cohomology group^{} valued in the sheaf
$\mathcal{F}$

## 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 | Cartan theorem B |
---|---|

Canonical name | CartanTheoremB |

Date of creation | 2013-03-22 17:39:13 |

Last modified on | 2013-03-22 17:39:13 |

Owner | jirka (4157) |

Last modified by | jirka (4157) |

Numerical id | 5 |

Author | jirka (4157) |

Entry type | Theorem |

Classification | msc 32Q28 |

Classification | msc 32C35 |

Synonym | Cartan’s theorem B |

Related topic | CartanTheoremA |