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### Colimits of quasi-coherent sheaves on a ringed space

Recall from the stacks project that a sheaf of modules $F$ on a ringed space $X$ is called quasi-coherent if there is an open covering $\{U_i\}$ such that each $F|_{U_i}$ has a presentation, i.e. is ...

**3**

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### Smooth submanifolds defined by Subrings

To be honest, I don't really know, whether or not the following is a research level
question:
Let $M$ be a smooth manifold, $C^\infty(M)$ the smooth function ring on $M$ and
suppose $R\subset ...

**5**

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**2**answers

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### Coherence for pull-backs and push-forwards

Let $p:X \to S$ and $q:Y\to S$ be two objects in the category of ringed spaces over the ringed space
$S$, and let $f:X \to Y$ be a morphism over $S$.
Given a sheaf $\mathcal{F}$ of ...

**11**

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### Cohomology of Structure Sheaves: Algebraic, Constructible and more

I am not an algebraic geometer, but I am a topologist who uses sheaves. I have studied some algebraic geometry and am interested in what happens as I reduce the amount of rigidity in the structure ...

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### quasi-coherent modules outside algebraic geometry?

Let $X$ be a ringed space. A quasi-coherent module on $X$ is a module which has locally a presentation, i.e. locally on $X$, it is the cokernel of a map between free modules. If $X$ is a scheme, then ...