The locally-ringed-spaces tag has no wiki summary.

**8**

votes

**1**answer

339 views

### Which local ringed spaces are schemes?

(This was originally asked on math.stackexchange, but didn't get any responses. I figured it might be worthwhile to move it here and try again.)
This paper gives a proof that the underlying ...

**3**

votes

**3**answers

446 views

### Are schemes pushouts of neighbourhoods and formal neighbourhoods?

Hello,
I have two questions, the first less important.
Let $X$ be a scheme, $x \in X$ a schematic point.
What is an elegant way of defining/characterizing the map $\operatorname{Spec}(O_{X,x}) ...

**12**

votes

**0**answers

457 views

### Riemannian manifolds etc. as locally ringed spaces ?

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 ...

**7**

votes

**3**answers

1k views

### Justification of the term “invertible sheaf”

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 ...

**6**

votes

**1**answer

540 views

### Examples of locally ringed spaces

I want to know more classes of examples of locally ringed spaces. The reason is that when I want to prove/disprove something about locally ringed spaces, my examples are often not eclectic enough. ...

**1**

vote

**2**answers

799 views

### Closed subschemes and pulling back the structure sheaf via the inclusion map

I would just like a clarification related to closed subschemes.
If $(X,{\cal O}_X)$ is a locally ringed space and $A\subset X$ is any subset with the subspace topology then $i^{-1}{\cal O}_X$ will be ...

**4**

votes

**2**answers

403 views

### Given a morphism from X to Y, when is the morphism from O_Y to the pushforward of O_X injective

I would like to know under what condition the morphism $\mathcal{O}_Y\longrightarrow f_\ast \mathcal{O}_X$ induced by a morphism $f:X\longrightarrow Y$ of schemes is injective.
Let me give an example ...

**20**

votes

**3**answers

1k views

### What is the right version of “partitions of unity implies vanishing sheaf cohomology”

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 ...