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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 of
holomorphic functions on (and subsequently the sheaf of holomorphic functions on a
complex manifold ) is
coherent.
[1]
[2]
See also
Note
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