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9 votes
1 answer
447 views

Results in “generalised smooth spaces” that did not hold in the case of smooth manifolds

Consider the category of smooth manifolds $\text{Man}$. I quote from n-lab page: Manifolds are fantastic spaces. It’s a pity that there aren’t more of them. I understand that this category $\text{...
Praphulla Koushik's user avatar
9 votes
1 answer
426 views

How to view $\textbf{Sh}(\textbf{CartSp})/X$ as "space" in its own right, étale machinery from abstract nonsense perspective for smooth manifolds

Let $\textbf{CartSp}$ be the category of spaces of the from $\mathbb{R}^n$ with smooth maps between them. This is a site with respect to (differentially) good open covers, so consider the Grothendieck ...
KeD's user avatar
  • 221
5 votes
1 answer
512 views

Residue of the canonical sheaf along subvariety

Let $S$ be a smooth projective surface over an algebraically closed field $k$ and $C \subset S$ a singular curve. Let us denote by $K_S$ the class of canonical divisor of $S$ and $\mathcal{O}(K_S)$ ...
user267839's user avatar
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