Dimension and depth inequalities over complete intersections
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917995146641408 |
|---|---|
| author | Bergh, Petter Andreas Jorgensen, David A. Thompson, Peder |
| author_facet | Bergh, Petter Andreas Jorgensen, David A. Thompson, Peder |
| contents | For a pair of finitely generated modules $M$ and $N$ over a codimension $c$ complete intersection ring $R$ with $\ell(M\otimes_RN)$ finite, we pay special attention to the inequality $\dim M+\dim N \leq \dim R +c$. In particular, we develop an extension of Hochster's theta invariant whose nonvanishing detects equality. In addition, we consider a parallel theory where dimension and codimension are replaced by depth and complexity, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_01384 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dimension and depth inequalities over complete intersections Bergh, Petter Andreas Jorgensen, David A. Thompson, Peder Commutative Algebra 13H15, 13D22, 13C40 For a pair of finitely generated modules $M$ and $N$ over a codimension $c$ complete intersection ring $R$ with $\ell(M\otimes_RN)$ finite, we pay special attention to the inequality $\dim M+\dim N \leq \dim R +c$. In particular, we develop an extension of Hochster's theta invariant whose nonvanishing detects equality. In addition, we consider a parallel theory where dimension and codimension are replaced by depth and complexity, respectively. |
| title | Dimension and depth inequalities over complete intersections |
| topic | Commutative Algebra 13H15, 13D22, 13C40 |
| url | https://arxiv.org/abs/2301.01384 |