List questions from homological-algebra

Published on 28 Mar 2026 - 6:11

239

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The structure of contractible complexes

Published on 19 Aug 2019 - 8:36

561

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Show that $\operatorname{Tor}(A, B)$ is always a torsion group

Published on 19 Aug 2019 - 17:39

551

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Vanishing Ext Group of Torsion-free and Skyscraper Sheaves?

Published on 27 Mar 2026 - 15:19

217

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The succession of the coefficient theorem is split but not naturally

Published on 20 Aug 2019 - 20:52

248

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Bott and Tu Spectral Sequence of a Double Complex

Published on 25 Mar 2026 - 13:05

165

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show that $ \text{Ext}^1(\mathbb{Q}, \mathbb{Z}) = \hat{\mathbb{Z}}/\mathbb{Z} = \mathbb{A}_f / \mathbb{Q} $

Published on 26 Mar 2026 - 7:58

135

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$R$ is local ring with residue field $k$ and $A$ is f.g. over $R$. Then $\operatorname{pd}(A)=0$ iff $\operatorname{Tor}_1^R(A,k)=0$.

Published on 22 Aug 2019 - 23:47

245

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Bott and Tu Proposition 12.1

Published on 25 Mar 2026 - 13:04

64

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On possible closure operation induced by derived functors

Published on 01 Apr 2026 - 7:04

37

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$K$ is DG-algebra, $H_\star(K)$ forms graded $R-$algebra. Why $1\in H_0(K)$ or $[1]\neq 0\in H_0(K)$?

Published on 24 Aug 2019 - 0:33

229

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Koszul exact sequence of vector bundle

Published on 27 Mar 2026 - 7:57

247

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How to show these properties of inverse limits?

Published on 28 Mar 2026 - 14:44

147

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Local cohomology modules and direct limits

Published on 28 Mar 2026 - 5:22

123

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On a particular kind of ideals in Noetherian local rings

Published on 25 Mar 2026 - 6:12

List Question

injective envelope in the category of left exact functors

The structure of contractible complexes

Show that $\operatorname{Tor}(A, B)$ is always a torsion group

Vanishing Ext Group of Torsion-free and Skyscraper Sheaves?

The succession of the coefficient theorem is split but not naturally

Bott and Tu Spectral Sequence of a Double Complex

show that $ \text{Ext}^1(\mathbb{Q}, \mathbb{Z}) = \hat{\mathbb{Z}}/\mathbb{Z} = \mathbb{A}_f / \mathbb{Q} $

$R$ is local ring with residue field $k$ and $A$ is f.g. over $R$. Then $\operatorname{pd}(A)=0$ iff $\operatorname{Tor}_1^R(A,k)=0$.

Bott and Tu Proposition 12.1

On possible closure operation induced by derived functors

$K$ is DG-algebra, $H_\star(K)$ forms graded $R-$algebra. Why $1\in H_0(K)$ or $[1]\neq 0\in H_0(K)$?

Koszul exact sequence of vector bundle

How to show these properties of inverse limits?

Local cohomology modules and direct limits

On a particular kind of ideals in Noetherian local rings

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