2
votes
0answers
55 views

Cohomology and quotients for the canonical topology

Recall that for any category $\mathcal C$, there is a unique finest topology, the canonical topology on $\mathcal C$ for which all representable functors are sheaves. I am interested in the example ...
0
votes
3answers
277 views

Higher cohomology of sheaves on a projective space

Let $S\subset\mathbb{P}^n$ be a finite set of $s$ reduced points. Let $\mathcal{I}$ be the ideal sheaf of $S$ in $\mathbb{P}^n$. We consider the sheaf ...
1
vote
1answer
267 views

Cohomology of tangent bundles

Let $X$ be a smooth scheme and $Z\subset X$ a smooth subscheme. Consider the blow-up $$\pi:\widetilde{X}:=Bl_{Z}X\rightarrow X$$ of $X$ along $Z$. What is the relation between the cohomology of the ...
1
vote
2answers
262 views

Cohomology of a cochain complex of acyclic sheaves

Ok, sort of as a follow up to my previous question, let's recall the de Rham-Weil theorem: Let $F$ be a sheaf on a topological space $X$ and let $\mathcal{L}^{\bullet}$ be an acyclic resolution of ...