Question

The definition of Cohen-Macaulay algebra

score 44 · Answer 1 · 2023-03-11 06:40:00

44

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The definition of Cohen-Macaulay algebra

Published on 11 Mar 2023 - 6:40

score 65 · Answer 2 · 2026-03-25 11:16:28

65

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On local rings $(R, \mathfrak m)$ such that $\text{Spec}(R)$ is disjoint union of $\text{Ass}(R)$ and $ \{\mathfrak m \}$

Published on 25 Mar 2026 - 11:16

score 49 · Answer 3 · 2023-04-23 15:51:12

49

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When is a Noetherian Standard graded algebra over a field Cohen-Macaulay? Any counter-example when it is not the case?

Published on 23 Apr 2023 - 15:51

score 66 · Answer 4 · 2023-05-14 12:16:39

66

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Cohen-Macaulay property of graded ideals

Published on 14 May 2023 - 12:16

score 65 · Answer 5 · 2026-03-25 06:07:12

65

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When $R/I \cong S/J$, where $R$ is Cohen-Macaulay, $S$ is regular local and $ht(J)=\mu(J)$

Published on 25 Mar 2026 - 6:07

score 96 · Answer 6 · 2026-03-25 06:07:03

96

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Existence of a proper birational morphism from a Gorenstein scheme, with trivial higher direct images, implies Cohen-Macaulay?

Published on 25 Mar 2026 - 6:07

score 26 · Answer 7 · 2023-07-18 10:54:35

26

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Connection between heights of $(U:_R E)$ and $(ann(E):_R ann(U))$ for torsion-free modules $U\subseteq E$ of constant rank

Published on 18 Jul 2023 - 10:54

score 144 · Answer 8 · 2026-03-25 12:29:22

144

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If a resolution $f:Y\to X$ satisfies $R^if_\omega_Y=0$ and $R^if_\mathcal{O}_Y=0$ for all $i>0$, then do we have $f_*\omega_Y=\omega_X$?

Published on 25 Mar 2026 - 12:29

score 57 · Answer 9 · 2023-09-16 09:38:53

57

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Non-toric ring which is Cohen-Macaulay

Published on 16 Sep 2023 - 9:38

score 87 · Answer 10 · 2023-10-10 04:44:59

87

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Example of noetherian local ring without Maximal Cohen-Macaulay modules.

Published on 10 Oct 2023 - 4:44

score 80 · Answer 11 · 2023-10-24 02:33:46

80

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Serre conditions and local isomorphisms

Published on 24 Oct 2023 - 2:33

score 73 · Answer 12 · 2023-10-25 02:19:34

73

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Embedding of modules of finite length

Published on 25 Oct 2023 - 2:19

score 55 · Answer 13 · 2023-10-30 10:39:04

55

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Homomorphisms between regular local rings with regular system of parameters

Published on 30 Oct 2023 - 10:39

score 77 · Answer 14 · 2023-10-30 19:04:44

77

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Tensor product of field with Noetherian ring is Cohen-Macaulay

Published on 30 Oct 2023 - 19:04

score 72 · Answer 15 · 2023-11-03 04:39:04

72

Views

Going mod an element which annihilates a prime ideal (Associated primes)

Published on 03 Nov 2023 - 4:39

List Question

The definition of Cohen-Macaulay algebra

On local rings $(R, \mathfrak m)$ such that $\text{Spec}(R)$ is disjoint union of $\text{Ass}(R)$ and $ \{\mathfrak m \}$

When is a Noetherian Standard graded algebra over a field Cohen-Macaulay? Any counter-example when it is not the case?

Cohen-Macaulay property of graded ideals

When $R/I \cong S/J$, where $R$ is Cohen-Macaulay, $S$ is regular local and $ht(J)=\mu(J)$

Existence of a proper birational morphism from a Gorenstein scheme, with trivial higher direct images, implies Cohen-Macaulay?

Connection between heights of $(U:_R E)$ and $(ann(E):_R ann(U))$ for torsion-free modules $U\subseteq E$ of constant rank

If a resolution $f:Y\to X$ satisfies $R^if_\omega_Y=0$ and $R^if_\mathcal{O}_Y=0$ for all $i>0$, then do we have $f_*\omega_Y=\omega_X$?

Non-toric ring which is Cohen-Macaulay

Example of noetherian local ring without Maximal Cohen-Macaulay modules.

Serre conditions and local isomorphisms

Embedding of modules of finite length

Homomorphisms between regular local rings with regular system of parameters

Tensor product of field with Noetherian ring is Cohen-Macaulay

Going mod an element which annihilates a prime ideal (Associated primes)

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