Question

A morphism of sheaves is an epimorphism if and only if it is surjective on the level of stalks

score 1.7k · Answer 1 · 2026-03-25 04:44:23

1.7k

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A morphism of sheaves is an epimorphism if and only if it is surjective on the level of stalks

Published on 25 Mar 2026 - 4:44

score 1.2k · Answer 2 · 2026-03-25 12:53:10

1.2k

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A characterization of pure sheaf

Published on 25 Mar 2026 - 12:53

score 91 · Answer 3 · 2026-03-29 12:04:47

91

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A simple question about Grothendieck topoi

Published on 29 Mar 2026 - 12:04

score 253 · Answer 4 · 2026-03-26 16:03:30

253

Views

Global sections and restrictions

Published on 26 Mar 2026 - 16:03

score 47 · Answer 5 · 2026-03-25 09:49:33

47

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Clarification in the definition of presheaf

Published on 25 Mar 2026 - 9:49

score 57 · Answer 6 · 2026-03-25 09:46:24

57

Views

Show bijective correspondence

Published on 25 Mar 2026 - 9:46

score 116 · Answer 7 · 2026-03-25 09:53:51

116

Views

Show a sequence of sheaves is exact

Published on 25 Mar 2026 - 9:53

score 39 · Answer 8 · 2017-01-27 05:33:54

39

Views

Let $f:(X,\mathcal{O}_X)\to(Y,\mathcal{O}_Y)$, $\mathscr{F}$ an $\mathcal{O}_Y$-module. How is $f^{-1}\mathscr{F}$ an $f^{-1}\mathcal{O}_Y$ module?

Published on 27 Jan 2017 - 5:33

score 243 · Answer 9 · 2026-03-26 09:20:43

243

Views

Strong Noetherian Property (terminology)

Published on 26 Mar 2026 - 9:20

score 85 · Answer 10 · 2017-01-28 04:09:11

85

Views

Let $(X,\mathcal{O})$ be a ringed space, and let $\mathcal{I}\le\mathcal{O}$ be a sheaf of ideals. Then is $\mathcal{I}^k$ a sheaf?

Published on 28 Jan 2017 - 4:09

score 31 · Answer 11 · 2017-01-26 20:36:09

31

Views

If $U\subset X$ is open, and $\mathscr{F}$ a sheaf on $X$, then $\mathscr{F}_U = (\mathscr{F}_U)_{\bar{U}}$

Published on 26 Jan 2017 - 20:36

score 80 · Answer 12 · 2017-01-29 16:48:21

80

Views

Classify locally constant sheaves

Published on 29 Jan 2017 - 16:48

score 117 · Answer 13 · 2017-01-29 17:16:30

117

Views

Equivalent definitions of sheafification?

Published on 29 Jan 2017 - 17:16

score 55 · Answer 14 · 2017-01-29 19:55:49

55

Views

Show that $f^{-1}\Omega_{\mathcal{O}_2/\mathcal{O}_1}=\Omega_{f^{-1}\mathcal{O}_2/f^{-1}\mathcal{O}_1}$

Published on 29 Jan 2017 - 19:55

score 75 · Answer 15 · 2017-01-31 18:32:21

75

Views

Does the functor $\mathbb{Z}_*: PSh(\mathbf{C})\to PSh^{Ab}(\mathbf{C})$ send sheaves to sheaves?

Published on 31 Jan 2017 - 18:32

List Question

A morphism of sheaves is an epimorphism if and only if it is surjective on the level of stalks

A characterization of pure sheaf

A simple question about Grothendieck topoi

Global sections and restrictions

Clarification in the definition of presheaf

Show bijective correspondence

Show a sequence of sheaves is exact

Let $f:(X,\mathcal{O}_X)\to(Y,\mathcal{O}_Y)$, $\mathscr{F}$ an $\mathcal{O}_Y$-module. How is $f^{-1}\mathscr{F}$ an $f^{-1}\mathcal{O}_Y$ module?

Strong Noetherian Property (terminology)

Let $(X,\mathcal{O})$ be a ringed space, and let $\mathcal{I}\le\mathcal{O}$ be a sheaf of ideals. Then is $\mathcal{I}^k$ a sheaf?

If $U\subset X$ is open, and $\mathscr{F}$ a sheaf on $X$, then $\mathscr{F}_U = (\mathscr{F}_U)_{\bar{U}}$

Classify locally constant sheaves

Equivalent definitions of sheafification?

Show that $f^{-1}\Omega_{\mathcal{O}_2/\mathcal{O}_1}=\Omega_{f^{-1}\mathcal{O}_2/f^{-1}\mathcal{O}_1}$

Does the functor $\mathbb{Z}_*: PSh(\mathbf{C})\to PSh^{Ab}(\mathbf{C})$ send sheaves to sheaves?

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