List questions from sheaf-theory

Published on 25 Mar 2026 - 19:10

233

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Why is the Grassmannian functor representable by a scheme?

Published on 25 Mar 2026 - 7:51

137

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Is $U\mapsto \mathcal F(U)\otimes_{\mathcal O_X(U)}\mathcal F(U)$ a presheaf or sheaf?

Published on 18 Jun 2019 - 9:10

38

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Do we have $\mathcal G=\mathcal H$?

Published on 18 Jun 2019 - 9:36

66

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Sheaf on the big site $\operatorname{Sch}/S$ induced by sheaf on $S$

Published on 25 Mar 2026 - 11:04

2.1k

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Pushforward of Coherent Sheaf

Published on 19 Jun 2019 - 11:56

1k

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Presheaf is a sheaf iff it preserves limits

Published on 20 Jun 2019 - 14:43

335

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Nakayama's Lemma, Stalks and Fibres (Hartshorne III.12.7.2)

Published on 20 Jun 2019 - 18:15

73

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Do we have $(gf)^\mathcal F=f^(g^*\mathcal F)$?

Published on 22 Jun 2019 - 14:44

50

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Is $i^*(\mathcal O_{\mathrm P_S^m}(1))$ an invertible $\mathcal O_X$-module?

Published on 22 Jun 2019 - 15:30

102

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Do we have $\mathcal O_X(1)(X)=S_1$?

Published on 25 Mar 2026 - 6:19

199

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Do we have $\mathit\Gamma_*(\mathcal O_X)\cong S$?

Published on 25 Mar 2026 - 6:24

418

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Category of sheaves on a topological space is not $\mathbf{AB4^{*}}$

Published on 23 Jun 2019 - 17:44

51

Views

Is a Locally Affine Ringed Space Noetherian?

Published on 25 Mar 2026 - 14:30

262

Views

Cohomology of Finitely Generated Ideal Sheaf

Published on 25 Mar 2026 - 12:40

List Question

What is the correct definition of the inverse image functor on sheaves of modules?

Why is the Grassmannian functor representable by a scheme?

Is $U\mapsto \mathcal F(U)\otimes_{\mathcal O_X(U)}\mathcal F(U)$ a presheaf or sheaf?

Do we have $\mathcal G=\mathcal H$?

Sheaf on the big site $\operatorname{Sch}/S$ induced by sheaf on $S$

Pushforward of Coherent Sheaf

Presheaf is a sheaf iff it preserves limits

Nakayama's Lemma, Stalks and Fibres (Hartshorne III.12.7.2)

Do we have $(gf)^\mathcal F=f^(g^*\mathcal F)$?

Is $i^*(\mathcal O_{\mathrm P_S^m}(1))$ an invertible $\mathcal O_X$-module?

Do we have $\mathcal O_X(1)(X)=S_1$?

Do we have $\mathit\Gamma_*(\mathcal O_X)\cong S$?

Category of sheaves on a topological space is not $\mathbf{AB4^{*}}$

Is a Locally Affine Ringed Space Noetherian?

Cohomology of Finitely Generated Ideal Sheaf

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