List questions from exact-sequence

Published on 13 Mar 2026 - 19:08

82

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Definition of exact sequence

Published on 27 Dec 2015 - 22:11

43

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Derived functors on 2 term exact sequence

Published on 26 Mar 2026 - 17:28

591

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Apply the functor $Hom(-,B)$ to the following exact sequence

Published on 02 Jan 2016 - 0:29

75

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Short exact sequence on $\mathbb{P}^1$

Published on 16 Jan 2016 - 3:53

199

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Determine which abelian groups can be the central term of this exact short sequence

Published on 16 Jan 2016 - 11:53

75

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Question on syzygies

Published on 17 Jan 2016 - 3:03

224

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For $x\in\operatorname{Ext}_R^1(C,A)$, how to construct an extension $0\to A\to B\to C\to 0$ such that $\partial (id_A)=x$?

Published on 26 Mar 2026 - 17:33

70

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Where am I making a mistake with $Ext^1(A,C)$?

Published on 17 Jan 2016 - 22:35

569

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Short exact sequence of $\mathbb{R}[X]$-modules that does not split

Published on 18 Jan 2016 - 16:49

85

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Intuition behind $Ext^1(A,\,C)$

Published on 26 Mar 2026 - 3:14

92

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$E_{p,q}^r$ spectral sequence. Find a l.e.s. $\cdots \to A_{p+1}\to E_{p+1,0}^2\xrightarrow{d_{p+1,0}^2} E_{p-1,1}^2\to A_p\to E_{p,0}^2\to\cdots$

Published on 19 Mar 2026 - 19:07

2.2k

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Let $A$ be a local ring, $M$ and $N$ finitely generated $A$-modules. Show that if $M \otimes N = 0$ then $M=0$ or $N=0$

Published on 30 Jan 2016 - 11:42

1.2k

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Exact Sequences of Modules and Rank

Published on 05 Feb 2016 - 9:40

765

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$\text{Hom}_{\mathcal{O}_X}(\cdot, \mathcal{G})$ is an exact functor

Published on 09 Feb 2016 - 2:06

List Question

Nonsplit extension of $\mathbb{Z}$ by itself

Definition of exact sequence

Derived functors on 2 term exact sequence

Apply the functor $Hom(-,B)$ to the following exact sequence

Short exact sequence on $\mathbb{P}^1$

Determine which abelian groups can be the central term of this exact short sequence

Question on syzygies

For $x\in\operatorname{Ext}_R^1(C,A)$, how to construct an extension $0\to A\to B\to C\to 0$ such that $\partial (id_A)=x$?

Where am I making a mistake with $Ext^1(A,C)$?

Short exact sequence of $\mathbb{R}[X]$-modules that does not split

Intuition behind $Ext^1(A,\,C)$

$E_{p,q}^r$ spectral sequence. Find a l.e.s. $\cdots \to A_{p+1}\to E_{p+1,0}^2\xrightarrow{d_{p+1,0}^2} E_{p-1,1}^2\to A_p\to E_{p,0}^2\to\cdots$

Let $A$ be a local ring, $M$ and $N$ finitely generated $A$-modules. Show that if $M \otimes N = 0$ then $M=0$ or $N=0$

Exact Sequences of Modules and Rank

$\text{Hom}_{\mathcal{O}_X}(\cdot, \mathcal{G})$ is an exact functor

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