Cartan theorem A

Let $\\mathcal{O}_{z}$ denote the ring of germs ofholomorphic functions at $z$

Theorem (Cartan).

Suppose $\\mathcal{F}$ is a coherent analytic sheaf on a Steinmanifold $M$ .For every $z\\in M$ , the the stalk ${\\mathcal{F}}_{z}$ is generated as an ${\\mathcal{O}}_{z}$ module by the germs at $z$ of the sections (http://planetmath.org/Sheaf) $\\Gamma(M,\\mathcal{F})$ .

Philosophically, this theorem says that there is good supply of of a coherent analytic sheaf on a Stein manifold.

References

1 Lars Hörmander.,North-Holland Publishing Company, New York, New York, 1973.
2 Steven G. Krantz.,AMS Chelsea Publishing, Providence, Rhode Island, 1992.

单词	CartanTheoremA
释义	Cartan theorem A Let $\\mathcal{O}_{z}$ denote the ring of germs ofholomorphic functions at $z$ Theorem (Cartan). Suppose $\\mathcal{F}$ is a coherent analytic sheaf on a Steinmanifold $M$ .For every $z\\in M$ , the the stalk ${\\mathcal{F}}_{z}$ is generated as an ${\\mathcal{O}}_{z}$ module by the germs at $z$ of the sections (http://planetmath.org/Sheaf) $\\Gamma(M,\\mathcal{F})$ . Philosophically, this theorem says that there is good supply of of a coherent analytic sheaf on a Stein manifold. References 1 Lars Hörmander.,North-Holland Publishing Company, New York, New York, 1973. 2 Steven G. Krantz.,AMS Chelsea Publishing, Providence, Rhode Island, 1992.
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