# Questions tagged [sheaf-cohomology]

In mathematics, sheaf cohomology is the aspect of sheaf theory, concerned with sheaves of abelian groups, that applies homological algebra to make possible effective calculation of the global sections of a sheaf F. (Def: http://en.m.wikipedia.org/wiki/Sheaf_cohomology)

707 questions
Filter by
Sorted by
Tagged with
1 vote
29 views

### First higher direct image of a constant sheaf

Let $X$, $F$ be manifolds and $f:X\times F\to X$ be a natural projection. Then is the first higher direct image of a constant sheaf $R^1f_*(\mathbb{Z}_{X\times F})$ also a constant sheaf on $X$ with ...
37 views

### Why is $H^0(X_n, \mathcal{O}_{X_n})$ a local artin ring.

Let $V$ be regular, proper and of dimension 2 over $S =$ spec $R$, for $R$ a complete discrete valuation ring with uniformizer $t$, maximal ideal $\mathfrak{m}$, and algebraically closed residue ...
101 views

### How do one show that the quotient space is a projective manifold?

I want to prove the following statement. Let $\Omega$ be a bounded domain, and $\Gamma \subset \text{Aut}(\Omega)$ be the subgroup acting totally discontinuously on $\Omega$ without fixed points such ...
• 51
62 views

97 views

• 179
74 views

40 views

### Doubts about a short exact sequence of sheaves

I am attending a course on Complex Manifolds and we are dealing with sheaves theory. Our professor made a statement which is not really clear to me, so I am hoping for some clarification here. Given ...
• 23.6k
1 vote
88 views

### Hartshorne problem III.4.4

Again I'm stuck on a problem in Hartshorne! In this problem we are supposed to show that if we take the limit of all coverings in on a topological space then the Cech cohomology agrees with derived ...
• 578
158 views

### An example that Čech cohomology is not equal to derived cohomology with on an affine scheme with Zariski topology.

There is an example in 3.1.10 $\mathbb{A}^1$-homotopy theory of schemes demonstrating that the Čech cohomology on an affine scheme with Zariski topology can be different from the derived cohomology. ...
• 1,466
1 vote
### Are stalks of q-singular cochain equal to 0?($q>0$)
Let $\mathcal{S}^{q}$ be the presheaf of singular q-cochains on a topological space $X$, that is the functor $\mathcal{S}^{q} \colon \mathcal{O}(X)^{op} \to \mathbb{Z}$-$\mathsf{Mod}$ which is given ...