In mathematics, the Oka coherence theorem, proved by Kiyoshi Oka (1950), states that the sheaf of holomorphic functions on (and subsequently the sheaf of holomorphic functions on a complex manifold ) is coherent.[1][2]
See also[edit]
- Cartan's theorems A and B
- Several complex variables
- GAGA
- Oka–Weil theorem
- Weierstrass preparation theorem
Note[edit]
- ^ Noguchi (2019)
- ^ In Oka (1950) paper it was called the idéal de domaines indéterminés.
References[edit]
- 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