List questions from sheaf-theory

Published on 17 Jan 2022 - 13:17

103

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$\mathscr{I}$ is injective iff for every $U \subseteq X$, $R \subseteq \mathbb{Z}_U$, and map $f: R \to \mathscr{I}$ extends to $\mathbb{Z}_U$.

Published on 19 Jan 2022 - 4:07

56

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$\mathbf{coim}(f) = \mathbf{im}(f)$ for sheave morphisms

Published on 22 Jan 2022 - 0:47

198

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Definition of a subsheaf, Bredon sheaf theory

Published on 25 Jan 2022 - 23:23

831

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Tensor with dual of locally free sheaf isomorphic to sheaf Hom

Published on 27 Jan 2022 - 0:53

325

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Hartshorne Exercise II.6.10 Proving existence of a filtration for coherent sheaves supported on a closed subscheme.

Published on 27 Mar 2026 - 6:52

517

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Why was O. Gabber not an author of the 1983's Faisceaux Pervers?

Published on 31 Jan 2022 - 14:56

117

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Does the (pseudo)functor that assigns a commutative monoid $M$ to the topos of $M\text{-Sets}$ preserve limits?

Published on 29 Mar 2026 - 9:11

150

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If $M$ is a compact Riemann surface, then $H^1(M,\mathbb R)\cong H^1(M,\mathcal O)$

Published on 08 Apr 2026 - 18:03

45

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Conditions for evaluation morphisms $H^{0}(X, -K_X) \rightarrow k^n$ to be surjective.

Published on 25 Mar 2026 - 17:34

69

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(co)algebras of the adjunction between presheaves and bundles

Published on 26 Mar 2026 - 7:59

115

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Locally free sheaf and locally constant system

Published on 27 Mar 2026 - 6:59

118

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Relation among Chern classes

Published on 27 Mar 2026 - 13:45

402

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Externalizing A Concrete Application of Double Negation Toposes

Published on 23 Feb 2026 - 19:19

65

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Twisted structure sheaves for $X=\operatorname{Spec} k$

Published on 26 Mar 2026 - 8:15

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Stalks of isomorphic presheaves

$\mathscr{I}$ is injective iff for every $U \subseteq X$, $R \subseteq \mathbb{Z}_U$, and map $f: R \to \mathscr{I}$ extends to $\mathbb{Z}_U$.

$\mathbf{coim}(f) = \mathbf{im}(f)$ for sheave morphisms

Definition of a subsheaf, Bredon sheaf theory

Tensor with dual of locally free sheaf isomorphic to sheaf Hom

Hartshorne Exercise II.6.10 Proving existence of a filtration for coherent sheaves supported on a closed subscheme.

Why was O. Gabber not an author of the 1983's Faisceaux Pervers?

Does the (pseudo)functor that assigns a commutative monoid $M$ to the topos of $M\text{-Sets}$ preserve limits?

If $M$ is a compact Riemann surface, then $H^1(M,\mathbb R)\cong H^1(M,\mathcal O)$

Conditions for evaluation morphisms $H^{0}(X, -K_X) \rightarrow k^n$ to be surjective.

(co)algebras of the adjunction between presheaves and bundles

Locally free sheaf and locally constant system

Relation among Chern classes

Externalizing A Concrete Application of Double Negation Toposes

Twisted structure sheaves for $X=\operatorname{Spec} k$

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