In mathematics, specifically algebraic geometry, the Oka coherence theorem, proved by Kiyoshi Oka in 1950, states that the sheaf O C n {\displaystyle {\mathcal {O}}_{\mathbb {C} ^{n}}} of holomorphic functions on C n {\displaystyle \mathbb {C} ^{n}} (and subsequently the sheaf O X {\displaystyle {\mathcal {O}}_{X}} of holomorphic functions on a complex manifold X {\displaystyle X} ) is coherent.
See also Cartan's theorems A and B Several complex variables GAGA Oka–Weil theorem Weierstrass preparation theorem
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