Oka coherence theorem

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