Questions tagged [locally-ringed-spaces]

I've asked this question https://math.stackexchange.com/questions/1407451/about-the-relation-between-the-categories-textsch-textlrs-and-text on math.stackexchange , however I don't think I will ...

This coming fall, I will be teaching a course on differential topology to a small group of strong students. In preparation for it, I'm trying to find a category $\mathrm{GDiff}$ with the following ...

There are several theorems I know of the form "Let $X$ be a locally ringed space obeying some condition like existence of partitions of unity. Let $E$ be a sheaf of $\mathcal{O}_X$ modules obeying ...

There are, among others, three general ways of equipping a "space" (which for the purposes of this question could be a topological space or a differentiable manifold, according to the case) with ...

Let $X$ be a locally ringed space (or a scheme) and $M,N$ two $\mathcal{O}_X$-modules such that $M \otimes N \cong \mathcal{O}_X$. Does it follow that $M$ is invertible in the usual sense, namely that ...

It is known that the natural functor of smooth functions from the category of smooth manifolds into the category of locally ringed spaces is a full embedding (see, for example, here). Is a similar ...