In mathematics, the Oka coherence theorem, proved by Kiyoshi Oka (1950), states that the sheaf of germs of holomorphic functions on over a complex manifold is coherent.[1][2]

See also

Note

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

References

  • Grauert, H.; Remmert, R. (6 December 2012). Coherent Analytic Sheaves. Springer. ISBN 978-3-642-69582-7.
  • Hörmander, Lars (1990), An introduction to complex analysis in several variables, Amsterdam: North-Holland, ISBN 978-0-444-88446-6, MR 0344507
  • Noguchi, Junjiro (2019), "A Weak Coherence Theorem and Remarks to the Oka Theory" (PDF), Kodai Math. J., 42 (3): 566–586, arXiv:1704.07726, doi:10.2996/kmj/1572487232, S2CID 119697608
  • Oka, Kiyoshi (1950), "Sur les fonctions analytiques de plusieurs variables. VII. Sur quelques notions arithmétiques", Bulletin de la Société Mathématique de France, 78: 1–27, doi:10.24033/bsmf.1408, ISSN 0037-9484, MR 0035831
  • Onishchik, A.L. (2001) [1994], "Coherent analytic sheaf", Encyclopedia of Mathematics, EMS Press


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