Cartan theorem A

Let 𝒪z denote the ring of germs of holomorphic functionsMathworldPlanetmath at z

Theorem (Cartan).

Suppose F is a coherent analytic sheaf on a Stein manifoldMathworldPlanetmath M. For every zM, the the stalk Fz is generated as an Oz module by the germs at z of the sections ( Γ(M,F).

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


  • 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 A
Canonical name CartanTheoremA
Date of creation 2013-03-22 17:39:10
Last modified on 2013-03-22 17:39:10
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 6
Author jirka (4157)
Entry type Theorem
Classification msc 32Q28
Classification msc 32C35
Synonym Cartan’s theorem A
Related topic CartanTheoremB