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单词 CartanTheoremA
释义

Cartan theorem A


Let 𝒪z denote the ring of germs ofholomorphic functionsMathworldPlanetmath at z

Theorem (Cartan).

Suppose F is a coherent analytic sheaf on a SteinmanifoldMathworldPlanetmath M.For every zM, the the stalk Fzis generated as an Oz module by the germs at zof the sections (http://planetmath.org/Sheaf) Γ(M,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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