List questions from quasicoherent-sheaves

Published on 05 May 2020 - 0:11

943

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Why is the pullback (between affine varieties) of a quasi coherent sheaf quasi coherent?

Published on 23 Feb 2026 - 10:05

70

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Show that $\oplus\widetilde{M}_{\alpha}\cong \widetilde{\oplus M_{\alpha}}$ with $M_{\alpha}$ $\mathcal{O}_{X}(X)$-modules.

Published on 04 Jun 2020 - 12:28

94

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Proving that a quasi-coherent $\mathcal{F}$ is coherent by looking at one affine covering

Published on 10 Jun 2020 - 5:41

38

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$f_*\mathcal{F}$ is quasi-coherent if $\mathcal{F}$ is quasi-coherent and $f$ is affine

Published on 10 Jun 2020 - 14:44

403

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Hartshorne 5.11 twisted sheaf

Published on 23 Jun 2020 - 17:44

91

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Katz's proof of Cartier's (descent) theorem

Published on 25 Mar 2026 - 11:54

96

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On global section of Hom-functor on quasi-coherent sheaves on a quasi-affine scheme

Published on 26 Jul 2020 - 17:41

200

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Explicit description of $\mathcal{O}_{\Bbb{P}^1}(-1)$ as a line bundle

Published on 25 Mar 2026 - 12:53

772

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Hartshorne Lemma II.5.3 Proof

Published on 22 Mar 2026 - 23:05

958

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Clarification on Ravi Vakil's AG notes, Exercise 13.3.H

Published on 22 Mar 2026 - 16:56

606

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Riemann-Roch equation for proper integral curves (not necessarily non-singular!)

Published on 25 Mar 2026 - 19:03

141

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Morphisms between quasi-coherent sheaves

Published on 25 Mar 2026 - 17:36

391

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Tensoring by locally free sheaves preserves quasi-isomorphism

Published on 25 Mar 2026 - 19:04

1.3k

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Category of quasicoherent sheaves not abelian

Published on 25 Mar 2026 - 19:04

List Question

Applications of fpqc descent of quasicoherent sheaves

Why is the pullback (between affine varieties) of a quasi coherent sheaf quasi coherent?

Show that $\oplus\widetilde{M}_{\alpha}\cong \widetilde{\oplus M_{\alpha}}$ with $M_{\alpha}$ $\mathcal{O}_{X}(X)$-modules.

Proving that a quasi-coherent $\mathcal{F}$ is coherent by looking at one affine covering

$f_*\mathcal{F}$ is quasi-coherent if $\mathcal{F}$ is quasi-coherent and $f$ is affine

Hartshorne 5.11 twisted sheaf

Katz's proof of Cartier's (descent) theorem

On global section of Hom-functor on quasi-coherent sheaves on a quasi-affine scheme

Explicit description of $\mathcal{O}_{\Bbb{P}^1}(-1)$ as a line bundle

Hartshorne Lemma II.5.3 Proof

Clarification on Ravi Vakil's AG notes, Exercise 13.3.H

Riemann-Roch equation for proper integral curves (not necessarily non-singular!)

Morphisms between quasi-coherent sheaves

Tensoring by locally free sheaves preserves quasi-isomorphism

Category of quasicoherent sheaves not abelian

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