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Cartan theorem B (Theorem)
Theorem 1 (Cartan)   Suppose $\mathcal{F}$ is a coherent analytic sheaf on a Stein manifold $M$ Then for $k > 0$ then \begin{equation*} H^k(M,\mathcal{F}) = 0 . \end{equation*}

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

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.




"Cartan theorem B" is owned by jirka.
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See Also: Cartan theorem A

Other names:  Cartan's theorem B
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Cross-references: sheaf, cohomology group, Stein manifold, coherent analytic sheaf
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This is version 2 of Cartan theorem B, born on 2007-12-03, modified 2007-12-12.
Object id is 10087, canonical name is CartanTheoremB.
Accessed 1100 times total.

Classification:
AMS MSC32C35 (Several complex variables and analytic spaces :: Analytic spaces :: Analytic sheaves and cohomology groups)
 32Q28 (Several complex variables and analytic spaces :: Complex manifolds :: Stein manifolds)

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