Question

On $\mathrm{Ext}_R^n(V,M)$ and $\mathrm{Tor}^R_n (V,M)$, where $M$ is an $R$-module with non-zero annihilator and $V$ is a $Q(R)$-vector space

score 160 · Answer 1 · 2026-04-16 13:53:12

160

Views

On $\mathrm{Ext}_R^n(V,M)$ and $\mathrm{Tor}^R_n (V,M)$, where $M$ is an $R$-module with non-zero annihilator and $V$ is a $Q(R)$-vector space

Published on 16 Apr 2026 - 13:53

score 106 · Answer 2 · 2026-04-15 21:00:44

106

Views

On derived functors of certain $\operatorname{Tor}_1$ and $\operatorname{Ext}^1$

Published on 15 Apr 2026 - 21:00

score 99 · Answer 3 · 2026-04-16 02:55:16

99

Views

Left derived functors vanish on a projective.

Published on 16 Apr 2026 - 2:55

score 693 · Answer 4 · 2026-04-15 20:49:17

693

Views

Direct limit of directed system of modules commutes with right derived functors of additive, covariant, left exact functor?

Published on 15 Apr 2026 - 20:49

score 297 · Answer 5 · 2026-04-16 09:25:28

297

Views

Right derived functors of the $I$-torsion functor and $\varinjlim \mathrm{Ext}^i_R(R/I^n,-)$ are naturally isomorphic?

Published on 16 Apr 2026 - 9:25

score 32 · Answer 6 · 2026-04-09 18:26:26

32

Views

Is $-\otimes ^L A/I$ a conservatice functor?

Published on 09 Apr 2026 - 18:26

score 87 · Answer 7 · 2026-04-12 15:51:43

87

Views

How to understand $k \otimes_R \alpha \cong k \oplus k$?

Published on 12 Apr 2026 - 15:51

score 594 · Answer 8 · 2026-04-17 05:50:07

594

Views

Weibel Exercise 2.4.3, dimension shift

Published on 17 Apr 2026 - 5:50

score 69 · Answer 9 · 2026-04-16 03:36:45

69

Views

In general, what's the relation between $\text{Ext}^n_R(A,B)$ and $\text{Ext}^n_R(B,A)$ (if any)?

Published on 16 Apr 2026 - 3:36

score 86 · Answer 10 · 2026-04-15 18:43:56

86

Views

$F(f)=0$, then $f=0$ where $0$ is the zero morphism for equivalent functors.

Published on 15 Apr 2026 - 18:43

score 115 · Answer 11 · 2026-04-12 08:05:46

115

Views

Snake lemma for derived functors

Published on 12 Apr 2026 - 8:05

score 125 · Answer 12 · 2026-04-15 11:07:38

125

Views

When $\textrm{Tor}_n^A(-,A/radA)\neq 0$? ($A$ a finite dimensional $K$-algebra)

Published on 15 Apr 2026 - 11:07

score 515 · Answer 13 · 2026-04-16 03:29:26

515

Views

Proof that Grothendieck category has enough injectives : about the functor $ \mathbf{M} $

Published on 16 Apr 2026 - 3:29

score 151 · Answer 14 · 2026-04-13 00:53:31

151

Views

Why do we want to compute derived functors via forgetful functors though easier?

Published on 13 Apr 2026 - 0:53

score 59 · Answer 15 · 2026-04-09 12:07:54

59

Views

Compute $Tor_i^{\mathbb Z/ 6 \mathbb Z}(\mathbb Z/ 2\mathbb Z, \mathbb Z/ 2\mathbb Z)$

Published on 09 Apr 2026 - 12:07

List Question

On $\mathrm{Ext}_R^n(V,M)$ and $\mathrm{Tor}^R_n (V,M)$, where $M$ is an $R$-module with non-zero annihilator and $V$ is a $Q(R)$-vector space

On derived functors of certain $\operatorname{Tor}_1$ and $\operatorname{Ext}^1$

Left derived functors vanish on a projective.

Direct limit of directed system of modules commutes with right derived functors of additive, covariant, left exact functor?

Right derived functors of the $I$-torsion functor and $\varinjlim \mathrm{Ext}^i_R(R/I^n,-)$ are naturally isomorphic?

Is $-\otimes ^L A/I$ a conservatice functor?

How to understand $k \otimes_R \alpha \cong k \oplus k$?

Weibel Exercise 2.4.3, dimension shift

In general, what's the relation between $\text{Ext}^n_R(A,B)$ and $\text{Ext}^n_R(B,A)$ (if any)?

$F(f)=0$, then $f=0$ where $0$ is the zero morphism for equivalent functors.

Snake lemma for derived functors

When $\textrm{Tor}_n^A(-,A/radA)\neq 0$? ($A$ a finite dimensional $K$-algebra)

Proof that Grothendieck category has enough injectives : about the functor $ \mathbf{M} $

Why do we want to compute derived functors via forgetful functors though easier?

Compute $Tor_i^{\mathbb Z/ 6 \mathbb Z}(\mathbb Z/ 2\mathbb Z, \mathbb Z/ 2\mathbb Z)$

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