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 157 · Answer 1 · 2019-03-04 02:29:02

157

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 04 Mar 2019 - 2:29

score 103 · Answer 2 · 2019-03-05 19:46:26

103

Views

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

Published on 05 Mar 2019 - 19:46

score 96 · Answer 3 · 2019-03-06 00:43:00

96

Views

Left derived functors vanish on a projective.

Published on 06 Mar 2019 - 0:43

score 690 · Answer 4 · 2019-03-07 01:55:24

690

Views

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

Published on 07 Mar 2019 - 1:55

score 294 · Answer 5 · 2019-03-15 07:43:44

294

Views

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

Published on 15 Mar 2019 - 7:43

score 30 · Answer 6 · 2019-03-30 17:10:53

30

Views

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

Published on 30 Mar 2019 - 17:10

score 84 · Answer 7 · 2019-04-05 09:11:31

84

Views

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

Published on 05 Apr 2019 - 9:11

score 591 · Answer 8 · 2019-04-09 10:32:23

591

Views

Weibel Exercise 2.4.3, dimension shift

Published on 09 Apr 2019 - 10:32

score 66 · Answer 9 · 2019-04-15 23:58:50

66

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 15 Apr 2019 - 23:58

score 83 · Answer 10 · 2019-04-20 23:02:07

83

Views

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

Published on 20 Apr 2019 - 23:02

score 112 · Answer 11 · 2019-05-01 17:38:15

112

Views

Snake lemma for derived functors

Published on 01 May 2019 - 17:38

score 123 · Answer 12 · 2019-06-01 22:51:26

123

Views

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

Published on 01 Jun 2019 - 22:51

score 512 · Answer 13 · 2019-06-04 08:36:20

512

Views

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

Published on 04 Jun 2019 - 8:36

score 148 · Answer 14 · 2019-06-08 19:37:26

148

Views

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

Published on 08 Jun 2019 - 19:37

score 56 · Answer 15 · 2019-06-16 17:35:31

56

Views

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

Published on 16 Jun 2019 - 17:35

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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