Oka coherence theorem

In mathematics, specifically algebraic geometry, the Oka coherence theorem, proved by Kiyoshi Oka in 1950,^[1] 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.^[2][3]

See also

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

Notes

References