User Alex

6 votes

2 answers

301 views

If Serre's intersection multiplicity $\chi(R/I, R/J)$ equals $\operatorname{length}_R (R/(I+J))$, then are $R/I, R/J$ Cohen-Macaulay?

asked Oct 5, 2022 at 0:58

6 votes

1 answer

338 views

When can we choose non-zero-divisor $x\in \mathfrak m$ in a reduced local ring $(R,\mathfrak m)$ such that $R/xR$ is also reduced?

asked Oct 9, 2022 at 23:56

3 votes

1 answer

197 views

Image, upto direct summands, of derived push-forward of resolution of singularities

asked Mar 11 at 2:52

3 votes

1 answer

129 views

Thick subcategory containment in bounded derived category vs. singularity category

asked Apr 16 at 19:37

2 votes

0 answers

75 views

Sum of Betti numbers and certain short exact sequence of modules of finite length over regular local ring

asked May 30 at 17:28

2 votes

0 answers

73 views

From exact triangles in the stable category of maximal Cohen--Macaulay modules to short exact sequences

asked Dec 24, 2023 at 4:29

2 votes

1 answer

206 views

Localization of quasi-excellent rings are quasi-excellent?

asked Jul 2 at 15:24

2 votes

0 answers

93 views

Minimal injective resolution and change of rings

asked Jul 7 at 16:57

2 votes

1 answer

112 views

Example of non injective module over Noetherian local ring with trivial vanishing against residue field?

asked Jul 13 at 20:44

2 votes

1 answer

388 views

When is Hilbert-Samuel multiplicity of a local ring non-increasing along localization at prime ideals?

asked Sep 29, 2022 at 23:32

1 vote

1 answer

88 views

Transcendence degree and Krull dimension for homomorphic images of power series rings

asked Jul 14 at 17:22

1 vote

1 answer

92 views

On analytic transcendence degree and Krull dimension for homomorphic images of power series rings

asked Jul 19 at 15:45

1 vote

0 answers

85 views

Is $(I(R:_{Q(R)} I))^n$ generated by $(fI)^n$ as $f$ varies over $(R:_{Q(R)} I)$?

asked Mar 18 at 10:25

1 vote

0 answers

80 views

Localization of totally acyclic complex or projective modules remain totally acyclic?

asked Jun 21 at 0:29

1 vote

0 answers

54 views

contravariant finiteness and limit closure: is there dual to a result of Crawley-Boevey?

asked Apr 22 at 9:01

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15 Questions

If Serre's intersection multiplicity $\chi(R/I, R/J)$ equals $\operatorname{length}_R (R/(I+J))$, then are $R/I, R/J$ Cohen-Macaulay?

When can we choose non-zero-divisor $x\in \mathfrak m$ in a reduced local ring $(R,\mathfrak m)$ such that $R/xR$ is also reduced?

Image, upto direct summands, of derived push-forward of resolution of singularities

Thick subcategory containment in bounded derived category vs. singularity category

Sum of Betti numbers and certain short exact sequence of modules of finite length over regular local ring

From exact triangles in the stable category of maximal Cohen--Macaulay modules to short exact sequences

Localization of quasi-excellent rings are quasi-excellent?

Minimal injective resolution and change of rings

Example of non injective module over Noetherian local ring with trivial vanishing against residue field?

When is Hilbert-Samuel multiplicity of a local ring non-increasing along localization at prime ideals?

Transcendence degree and Krull dimension for homomorphic images of power series rings

On analytic transcendence degree and Krull dimension for homomorphic images of power series rings

Is $(I(R:_{Q(R)} I))^n$ generated by $(fI)^n$ as $f$ varies over $(R:_{Q(R)} I)$?

Localization of totally acyclic complex or projective modules remain totally acyclic?

contravariant finiteness and limit closure: is there dual to a result of Crawley-Boevey?