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Questions tagged [sheaf-cohomology]

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4 votes
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Resolution of constant sheaf by $L^2$ function sheaves

Let $X$ be a compact Hausdorff space equipped with a Radon measure of full support. Then $U\mapsto L^2(U)$ is a fine sheaf, hence can be taken for a first step in an acyclic resolution of the constant ...
Antonius's user avatar
  • 492
3 votes
0 answers
133 views

Grothendieck spectral sequence (cohomology version) for posets with functor coefficient

In this paper, Quillen mentioned a spectral sequence as follows. Let $f:X\to Y$ is a poset map and $\mathcal{F}:X\to Ab$, where $Ab$ is the category of abelian groups, a functor which is contravariant ...
GURI920826's user avatar
2 votes
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Are maps between cohomology of homogeneous vector bundles morphisms of representations?

Let $X = G/P$ a rational homogeneous variety, e.g. a grassmannian. Consider a short exact sequence $$ 0 \longrightarrow E_1 \longrightarrow E_2 \longrightarrow E_3 \longrightarrow 0$$ where $E_i$ are ...
AleK3's user avatar
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