Canonical traces of graded fiber products: applications to disconnected Stanley--Reisner rings
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918470340313088 |
|---|---|
| author | Kumashiro, Shinya Miyashita, Sora |
| author_facet | Kumashiro, Shinya Miyashita, Sora |
| contents | Recent work by Miyashita and Varbaro classified the canonical traces of Stanley--Reisner rings that are Gorenstein on the punctured spectrum, under the Cohen--Macaulay assumption. The purpose of this paper is to generalize the result to the non--Cohen--Macaulay case. First, we establish an explicit formula for the canonical trace of graded fiber products of Noetherian rings and apply it to Stanley--Reisner rings of disconnected simplicial complexes. This allows us to reduce the problem to the case of connected simplicial complexes. In that case, we succeeded in giving a complete classification without assuming the Cohen--Macaulay property. Finally, we combine these results to obtain a classification for disconnected simplicial complexes, complementing the work of Miyashita and Varbaro. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04899 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Canonical traces of graded fiber products: applications to disconnected Stanley--Reisner rings Kumashiro, Shinya Miyashita, Sora Commutative Algebra Primary 13H10, 13A02, Secondary 05E40 Recent work by Miyashita and Varbaro classified the canonical traces of Stanley--Reisner rings that are Gorenstein on the punctured spectrum, under the Cohen--Macaulay assumption. The purpose of this paper is to generalize the result to the non--Cohen--Macaulay case. First, we establish an explicit formula for the canonical trace of graded fiber products of Noetherian rings and apply it to Stanley--Reisner rings of disconnected simplicial complexes. This allows us to reduce the problem to the case of connected simplicial complexes. In that case, we succeeded in giving a complete classification without assuming the Cohen--Macaulay property. Finally, we combine these results to obtain a classification for disconnected simplicial complexes, complementing the work of Miyashita and Varbaro. |
| title | Canonical traces of graded fiber products: applications to disconnected Stanley--Reisner rings |
| topic | Commutative Algebra Primary 13H10, 13A02, Secondary 05E40 |
| url | https://arxiv.org/abs/2506.04899 |