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Let $X$ be a locally finite type scheme over $\mathbb C$.

I'm looking for the analogue of the notion "finite type" for $X^{an}$ and an SGA 1 Exp. XII type of criterion which says that

The scheme $X$ is finite type over $\mathbb {C}$ if and only if the complex analytic space $X^{an}$ is of "finite type".

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    $\begingroup$ It seems unlikely. Analytification is compatible with the formation of irreducible components (analytic theory of which is developed in the book "Coherent Analytic Sheaves") as well as the underlying reduced space and normalization (by excellence) and smooth locus. Thus, a necessary condition is that $X^{\rm{an}}$ has only finitely many irreducible components, in which case by passing to the smooth locus in connected components of the normalization the task reduces to the smooth connected case. Alas, that seems no easier. But is there an actual context where such a criterion would be useful? $\endgroup$
    – nfdc23
    Commented Oct 2, 2016 at 16:09

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