A sharp bound for the Frobenius test exponents in generalized Cohen-Macaulay local rings
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918529129775104 |
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| author | Huong, Duong Thi Quy, Pham Hung |
| author_facet | Huong, Duong Thi Quy, Pham Hung |
| contents | Let $(R,\frak m)$ be a generalized Cohen-Macaulay local ring of prime characteristic $p$. In this paper we give a sharp bound for the Frobenius test exponent of parameter ideals. Namely, we prove that $$\mathrm{Fte}(R) \le \lceil \log_p(2n_0)\rceil + \mathrm{HSL}(R),$$ where $n_0$ is the integer such that $\frak m^{n_0} \, H^i_{\frak m}(R) = 0$ for all $i < \mathrm{dim}(R)$, and $\lceil x\rceil$ is the smallest integer that is greater than or equal to $x$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29544 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A sharp bound for the Frobenius test exponents in generalized Cohen-Macaulay local rings Huong, Duong Thi Quy, Pham Hung Commutative Algebra 13A35, 13D45 Let $(R,\frak m)$ be a generalized Cohen-Macaulay local ring of prime characteristic $p$. In this paper we give a sharp bound for the Frobenius test exponent of parameter ideals. Namely, we prove that $$\mathrm{Fte}(R) \le \lceil \log_p(2n_0)\rceil + \mathrm{HSL}(R),$$ where $n_0$ is the integer such that $\frak m^{n_0} \, H^i_{\frak m}(R) = 0$ for all $i < \mathrm{dim}(R)$, and $\lceil x\rceil$ is the smallest integer that is greater than or equal to $x$. |
| title | A sharp bound for the Frobenius test exponents in generalized Cohen-Macaulay local rings |
| topic | Commutative Algebra 13A35, 13D45 |
| url | https://arxiv.org/abs/2605.29544 |