Question

Is there a computationally cleaner way of working with inverse image functor $f^{-1}\mathcal{O}_Y$ in the category of schemes?

score 174 · Answer 1 · 2024-01-30 17:26:29

174

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Is there a computationally cleaner way of working with inverse image functor $f^{-1}\mathcal{O}_Y$ in the category of schemes?

Published on 30 Jan 2024 - 17:26

score 69 · Answer 2 · 2024-02-02 05:27:53

69

Views

Computing direct limit in sheaves

Published on 02 Feb 2024 - 5:27

score 70 · Answer 3 · 2026-02-23 02:52:55

70

Views

How does one define the observable presheaf?

Published on 23 Feb 2026 - 2:52

score 28 · Answer 4 · 2026-02-23 08:24:25

28

Views

Extension of a distinguished base in Vakil's notes

Published on 23 Feb 2026 - 8:24

score 122 · Answer 5 · 2026-03-26 06:21:22

122

Views

Is there a non-coherent subsheaf of $\mathscr{O}(-1)$ on $\mathbb{P}^1$

Published on 26 Mar 2026 - 6:21

score 85 · Answer 6 · 2026-03-26 03:02:32

85

Views

Vakil's Generalization of QCQS Lemma

Published on 26 Mar 2026 - 3:02

score 78 · Answer 7 · 2026-03-25 09:37:18

78

Views

rank of an $\mathcal{O}_X$-module being constant

Published on 25 Mar 2026 - 9:37

score 69 · Answer 8 · 2024-02-08 23:42:20

69

Views

Necessity of $X$ being reduced in Hartshorne Exercise II.4.2

Published on 08 Feb 2024 - 23:42

score 61 · Answer 9 · 2026-02-23 19:24:02

61

Views

Is there actually any bijection between characters and global sections of the spectral presheaf?

Published on 23 Feb 2026 - 19:24

score 77 · Answer 10 · 2024-02-10 22:56:05

77

Views

How does one go about proving that $f^{-1}\mathcal{G}$ is an $f^{-1}\mathcal{O}_Y$-module?

Published on 10 Feb 2024 - 22:56

score 115 · Answer 11 · 2024-02-13 13:41:07

Showing that for an $\mathcal{O}_X$-module $\mathcal{F}$ we have $\operatorname{Hom}(\mathcal{O}_X, \mathcal{F}) \cong \mathcal{F}(X)$.

score 66 · Answer 12 · 2024-02-14 15:41:44

66

Views

Global sections of a curve compoare to global sections of the reduced curve

Published on 14 Feb 2024 - 15:41

score 42 · Answer 13 · 2026-03-25 06:00:26

42

Views

Isomorphism between Tangent Sheaf and Cotangent Sheaf

Published on 25 Mar 2026 - 6:00

score 112 · Answer 14 · 2026-03-29 18:32:19

112

Views

For which sites are all sheaves connected (as presheaves)?

Published on 29 Mar 2026 - 18:32

score 73 · Answer 15 · 2024-02-17 11:39:22

73

Views

Different definitions of a sheaf

Published on 17 Feb 2024 - 11:39

List Question

Is there a computationally cleaner way of working with inverse image functor $f^{-1}\mathcal{O}_Y$ in the category of schemes?

Computing direct limit in sheaves

How does one define the observable presheaf?

Extension of a distinguished base in Vakil's notes

Is there a non-coherent subsheaf of $\mathscr{O}(-1)$ on $\mathbb{P}^1$

Vakil's Generalization of QCQS Lemma

rank of an $\mathcal{O}_X$-module being constant

Necessity of $X$ being reduced in Hartshorne Exercise II.4.2

Is there actually any bijection between characters and global sections of the spectral presheaf?

How does one go about proving that $f^{-1}\mathcal{G}$ is an $f^{-1}\mathcal{O}_Y$-module?

Showing that for an $\mathcal{O}_X$-module $\mathcal{F}$ we have $\operatorname{Hom}(\mathcal{O}_X, \mathcal{F}) \cong \mathcal{F}(X)$.

Global sections of a curve compoare to global sections of the reduced curve

Isomorphism between Tangent Sheaf and Cotangent Sheaf

For which sites are all sheaves connected (as presheaves)?

Different definitions of a sheaf

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