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Oka coherence theorem

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Theorem in complex analysis about the sheaf of holomorphic functions

In mathematics, the Oka coherence theorem, proved by Kiyoshi Oka (1950), states that the sheaf O C n {\displaystyle {\mathcal {O}}_{\mathbb {C} ^{n}}} of holomorphic functions on C n {\displaystyle \mathbb {C} ^{n}} (and subsequently the sheaf O X {\displaystyle {\mathcal {O}}_{X}} of holomorphic functions on a complex manifold X {\displaystyle X} ) is coherent.

See also

Note

  1. Noguchi (2019)
  2. In Oka (1950) paper it was called the idéal de domaines indéterminés.

References


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