# Cartan theorem B

###### Theorem (Cartan).

Suppose $\mathcal{F}$ is a coherent analytic sheaf on a Stein manifold $M$. Then for $k>0$, 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 CartanTheoremB 2013-03-22 17:39:13 2013-03-22 17:39:13 jirka (4157) jirka (4157) 5 jirka (4157) Theorem msc 32Q28 msc 32C35 Cartan’s theorem B CartanTheoremA