Question

Tor$^{R}_{n+1}(k,k)=0$ implies Pd$_RM\leq n$ for any $R$-module $M$?

score 237 · Answer 1 · 2026-03-25 17:22:26

237

Views

Tor$^{R}_{n+1}(k,k)=0$ implies Pd$_RM\leq n$ for any $R$-module $M$?

Published on 25 Mar 2026 - 17:22

score 70 · Answer 2 · 2019-08-11 20:40:56

70

Views

Why do I expect the pushout is the same?

Published on 11 Aug 2019 - 20:40

score 74 · Answer 3 · 2019-08-11 23:40:28

74

Views

Universal delta functor vanishing between some indices?

Published on 11 Aug 2019 - 23:40

score 92 · Answer 4 · 2019-08-12 00:42:17

92

Views

For each short eaxct sequence $0\to B\to C\to D\to 0$ there is a naturally associated exact sequence...

Published on 12 Aug 2019 - 0:42

score 205 · Answer 5 · 2026-03-25 11:06:38

205

Views

Motivation/intuition behind the definition of delta-functors and related concepts

Published on 25 Mar 2026 - 11:06

score 212 · Answer 6 · 2019-08-13 19:56:28

212

Views

Relation between global dimension and sup of injective dimensions of $R/I$

Published on 13 Aug 2019 - 19:56

score 67 · Answer 7 · 2019-08-14 20:58:08

67

Views

quasi-Frobenius iff Frobenius iff $\operatorname{ann}(m)\cong R/m$. its relation to algebraic geometry

Published on 14 Aug 2019 - 20:58

score 46 · Answer 8 · 2026-03-28 02:04:33

46

Views

How do you do simplicial homology with $0, 1$ coefficients?

Published on 28 Mar 2026 - 2:04

score 501 · Answer 9 · 2026-03-27 14:58:54

501

Views

$A$ is torsion free iff $Tor(A, B) = 0$ for all $B$ .

Published on 27 Mar 2026 - 14:58

score 34 · Answer 10 · 2019-08-18 03:18:24

34

Views

A morphism between two free resolutions of an Abelian group is unique except homotopies of chain complexes.

Published on 18 Aug 2019 - 3:18

score 56 · Answer 11 · 2019-08-18 15:39:33

56

Views

Which subcategory of the derived category of an algebra has a Serre functor?

Published on 18 Aug 2019 - 15:39

score 25 · Answer 12 · 2019-08-18 17:43:24

25

Views

Why to consider the map $T\otimes_R(U(M))\to T\otimes_R(U(M))$ by $t\otimes m\to (t\otimes m-1\otimes tm)$?

Published on 18 Aug 2019 - 17:43

score 42 · Answer 13 · 2019-08-18 20:03:27

42

Views

$h_:S_(X\times Y)\to S_(X\times Y)$ a homomorphism of natural chain complexes. If $h_0=Id$, show that $h_$ is homotopic to $Id$

Published on 18 Aug 2019 - 20:03

score 159 · Answer 14 · 2026-03-26 06:20:00

159

Views

Wrong Problem in Dummit and Foote - What could be correct?

Published on 26 Mar 2026 - 6:20

score 48 · Answer 15 · 2019-08-18 23:04:15

48

Views

How to prove for f.g. module $A$ over noetherian commutative local ring $R$ with $x\in NZD(R)\cap NZD(A)\cap m$, $id_R(A)=id_{R/x}(A/xA)$?

Published on 18 Aug 2019 - 23:04

List Question

Tor$^{R}_{n+1}(k,k)=0$ implies Pd$_RM\leq n$ for any $R$-module $M$?

Why do I expect the pushout is the same?

Universal delta functor vanishing between some indices?

For each short eaxct sequence $0\to B\to C\to D\to 0$ there is a naturally associated exact sequence...

Motivation/intuition behind the definition of delta-functors and related concepts

Relation between global dimension and sup of injective dimensions of $R/I$

quasi-Frobenius iff Frobenius iff $\operatorname{ann}(m)\cong R/m$. its relation to algebraic geometry

How do you do simplicial homology with $0, 1$ coefficients?

$A$ is torsion free iff $Tor(A, B) = 0$ for all $B$ .

A morphism between two free resolutions of an Abelian group is unique except homotopies of chain complexes.

Which subcategory of the derived category of an algebra has a Serre functor?

Why to consider the map $T\otimes_R(U(M))\to T\otimes_R(U(M))$ by $t\otimes m\to (t\otimes m-1\otimes tm)$?

$h_:S_(X\times Y)\to S_(X\times Y)$ a homomorphism of natural chain complexes. If $h_0=Id$, show that $h_$ is homotopic to $Id$

Wrong Problem in Dummit and Foote - What could be correct?

How to prove for f.g. module $A$ over noetherian commutative local ring $R$ with $x\in NZD(R)\cap NZD(A)\cap m$, $id_R(A)=id_{R/x}(A/xA)$?

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