Oka coherence theorem
From HandWiki
Short description: 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 [math]\displaystyle{ \mathcal{O} := \mathcal{O}_{\mathbb{C}_n} }[/math] of germs of holomorphic functions on [math]\displaystyle{ \mathbb{C}^n }[/math] over a complex manifold is coherent.[1][2]
See also
- Cartan's theorems A and B
- Several complex variables
- GAGA
- Oka–Weil theorem
- Weierstrass preparation theorem
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
- Noguchi, Junjiro (2019), "A Weak Coherence Theorem and Remarks to the Oka Theory", Kodai Math. J. 42 (3): 566–586, doi:10.2996/kmj/1572487232, https://www.ms.u-tokyo.ac.jp/~noguchi/WeakcohOka_3.pdf
- 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, http://www.numdam.org/item?id=BSMF_1950__78__1_0
- Hazewinkel, Michiel, ed. (2001), "Coherent analytic sheaf", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=c/c022990
 |  |
