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Results tagged with sheaf-cohomology
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user 24965
2
votes
0
answers
248
views
Is there a by-hand prove that $\Gamma(\mathbb{C}P^n,E)$ is finite dimensional for a holomorp...
Please let me know whether this question is suitable for Mathoverflow.
Let $E$ be a finite holomorphic vector bundle (or more generally a coherent analytic sheaf) on a compact complex manifold $X$. B …
- 9,019
3
votes
1
answer
505
views
For what kind of sheaves can we always extend a sheaf map from a closed subset to the whole ...
Let $X$ be a topological space. We know that a sheaf on $X$ is call soft if for any closed subset $Z$ of $X$, a section on $Z$ can be always extend to a section on $X$.
Now we consider a similar pr …
- 9,019
3
votes
1
answer
339
views
Is any element in $H^2_{et}(X,\mathcal{O}_X^*)$ locally trivial in the Zariski topology?
Let $X$ be an algebraic variety over a field $k$ and we consider the cohomological Brauer group $H^2_{et}(X,\mathcal{O}_X^*)$.
For any element $\alpha \in H^2_{et}(X,\mathcal{O}_X^*)$ and any closed …
- 9,019
5
votes
0
answers
606
views
Does the higher cohomology of a quasi-coherent sheaf on a Stein manifold vanish?
It is a well-known result in algebraic geometry that if $X$ is an affine scheme and $\mathcal{F}$ is a quasi-coherent sheaf on $X$, then the higher cohomologies of $\mathcal{F}$ vanish, i.e.
$$
H^i(X, …
- 9,019