All Questions

I will write $\operatorname{Diff}$ to denote a category of generalized smooth spaces e.g. $Sh(\mathsf{CartSp})$. Is there a version of $\operatorname{Diff}$ for which there exists a functor $\mathcal{...

My question is about whether it's more natural to see manifolds as ringed spaces or as locally ringed spaces. I think I have arguments for both points of view. On the one hand, it's reasonable to ...

Let $X$ be a locally ringed space. We have for a point $p$ the exact sequence $$0\to \mathfrak{m}_p^2\to \mathfrak{m}_p\to \mathfrak{m}_p/\mathfrak{m}_p^2 \to 0$$ where $\mathfrak{m}_p$ is the maximal ...

Let $X$ be a complex manifold, $F$ a bounded complex of $\Bbb C_X$-modules with constructible cohomology. If the set $\{x: F_x\neq0\}$ is relatively open (i.e. open in its closure), is the same true ...