Oka coherence theorem

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

• Cartan's theorems A and B
• Several complex variables
• GAGA
• Oka–Weil theorem
• Weierstrass preparation theorem