List questions from sheaf-cohomology

Published on 26 Mar 2026 - 21:27

351

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Kunneth formula for Čech cohomology

Published on 06 Jun 2021 - 14:32

384

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Calculating Sheaf Cohomology of Canonical Bundle over a Curve

Published on 08 Jun 2021 - 13:47

134

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$X$ rational surface, $\mathcal{F}$ nef, then $h^2(X,\mathcal{F})=0$

Published on 27 Mar 2026 - 5:39

95

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Why is $Mor_S(Spec R,SpecSym_{\mathcal{O}_S}\mathcal{Q})\cong Hom_{\mathcal{O}_S-\operatorname{mod}}(\mathcal{Q},f_{*}\mathcal{O}_{R})$?

Published on 10 Jun 2021 - 19:35

78

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Why does $R^{1}\pi_{S*}\mathcal{F}(r)$ vanish for large-enough $r$ if $\mathcal{F}$ is coherent?

Published on 26 Mar 2026 - 21:27

161

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Does a category of modules in an elementary topos have enough injectives?

Published on 17 Jun 2021 - 17:30

286

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Considering Long exact sequence of cohomology

Published on 01 Jul 2021 - 1:24

80

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Derived functor of $H^0$

Published on 27 Mar 2026 - 10:16

256

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Hodge decomposition.

Published on 27 Mar 2026 - 16:19

87

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Representing elements of $H^1(X, K_X)$ on a curve

Published on 27 Mar 2026 - 22:30

54

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How should I think of the nearby cycle $\mathrm R\Psi\overline{\mathbb Q_{\ell}}$ with its Galois action on a smooth projective scheme?

Published on 27 Mar 2026 - 9:48

285

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A naive question about the Godement resolution

Published on 21 Jul 2021 - 17:20

183

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Induced map on Cartan-Eilenberg resolutions through an exact functor

Published on 22 Jul 2021 - 14:22

59

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Cartan's theorem proof

Published on 30 Jul 2021 - 21:22

List Question

What is the difference between the Grothendieck and the Čech cohomology?

Kunneth formula for Čech cohomology

Calculating Sheaf Cohomology of Canonical Bundle over a Curve

$X$ rational surface, $\mathcal{F}$ nef, then $h^2(X,\mathcal{F})=0$

Why is $Mor_S(Spec R,SpecSym_{\mathcal{O}_S}\mathcal{Q})\cong Hom_{\mathcal{O}_S-\operatorname{mod}}(\mathcal{Q},f_{*}\mathcal{O}_{R})$?

Why does $R^{1}\pi_{S*}\mathcal{F}(r)$ vanish for large-enough $r$ if $\mathcal{F}$ is coherent?

Does a category of modules in an elementary topos have enough injectives?

Considering Long exact sequence of cohomology

Derived functor of $H^0$

Hodge decomposition.

Representing elements of $H^1(X, K_X)$ on a curve

How should I think of the nearby cycle $\mathrm R\Psi\overline{\mathbb Q_{\ell}}$ with its Galois action on a smooth projective scheme?

A naive question about the Godement resolution

Induced map on Cartan-Eilenberg resolutions through an exact functor

Cartan's theorem proof

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