A Buchsbaum theory for Frobenius closure
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912931281633280 |
|---|---|
| author | Goel, Kriti Maddox, Kyle Miller, Lance Edward Quy, Pham Hung Simpson, Austyn |
| author_facet | Goel, Kriti Maddox, Kyle Miller, Lance Edward Quy, Pham Hung Simpson, Austyn |
| contents | We give a partial characterization for when the difference $e(\mathfrak{q})-\ell_R(R/\mathfrak{q}^F)$ is independent of the choice of parameter ideal $\mathfrak{q}\subseteq R$ in an excellent equidimensional local ring $(R,\mathfrak{m})$ of prime characteristic $p>0$. Here, $\mathfrak{q}^F$ is the Frobenius closure of $\mathfrak{q}$ and $e(\mathfrak{q})$ denotes the Hilbert--Samuel multiplicity of $\mathfrak{q}$. In addition to ideal-theoretic equivalences, our characterization involves the derived category and is motivated by Schenzel's criterion of the Buchsbaum property as well as similar results of Ma-Quy in the setting of tight closure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03947 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Buchsbaum theory for Frobenius closure Goel, Kriti Maddox, Kyle Miller, Lance Edward Quy, Pham Hung Simpson, Austyn Commutative Algebra 13A35, 13H10, 13D45 We give a partial characterization for when the difference $e(\mathfrak{q})-\ell_R(R/\mathfrak{q}^F)$ is independent of the choice of parameter ideal $\mathfrak{q}\subseteq R$ in an excellent equidimensional local ring $(R,\mathfrak{m})$ of prime characteristic $p>0$. Here, $\mathfrak{q}^F$ is the Frobenius closure of $\mathfrak{q}$ and $e(\mathfrak{q})$ denotes the Hilbert--Samuel multiplicity of $\mathfrak{q}$. In addition to ideal-theoretic equivalences, our characterization involves the derived category and is motivated by Schenzel's criterion of the Buchsbaum property as well as similar results of Ma-Quy in the setting of tight closure. |
| title | A Buchsbaum theory for Frobenius closure |
| topic | Commutative Algebra 13A35, 13H10, 13D45 |
| url | https://arxiv.org/abs/2602.03947 |