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Inverse systems of projective schemes appear in several contexts, for example: in constructing the Zariski-Riemann space of a projective variety, in studying subvarieties of a projective variety ...

It is known that the category of schemes is not cocomplete (e.g. see this question: Colimits of schemes). However, do diagrams of schemes for which every morphism is etale have colimits? More ...

The title question is true in the setting of ordinary limits and ordinary schemes; that is, given an inverse limit of schemes along affine maps, the limit still lives in the category of schemes. I'd ...

Let $C$ be a category, and $\Gamma$ a graph in $C$. Under good conditions it makes sense to talk about the limit $\lim \Gamma$ of $\Gamma$ in $C$. Suppose $\Gamma$ is the union of two subgraphs $\...