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Cartan theorem B

(Theorem)

Theorem 1 (Cartan) Suppose $\mathcal{F}$ is a coherent analytic sheaf on a Stein manifold . Then for , then

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

Here, $H^k(M,\mathcal{F})$ is the th 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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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 570 times total.

Classification:

AMS MSC:	32C35 (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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