= Coherent analytic sheaf
{title2=$\mathcal F\text{ a coherent }\mathcal O_X\text{-module}$}
On a <complex manifold>, a sheaf of modules over the <sheaf of holomorphic functions> is coherent analytic if it is locally finitely generated and the kernel of every morphism $\mathcal O^r\to\mathcal F$ is locally finitely generated. The structure sheaf and locally free finite-rank sheaves are examples. <Cartan theorem B> gives vanishing of their higher <sheaf cohomology> on a <Stein manifold>.
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