On the test properties of the Frobenius endomorphism
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910173485858816 |
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| author | Celikbas, Olgur Sadeghi, Arash Yao, Yongwei |
| author_facet | Celikbas, Olgur Sadeghi, Arash Yao, Yongwei |
| contents | In this paper, we prove two theorems concerning the test properties of the Frobenius endomorphism over commutative Noetherian local rings of prime characteristic $p$. Our first theorem generalizes a result of Funk-Marley on the vanishing of Ext and Tor modules, while our second theorem generalizes one of our previous results on maximal Cohen-Macaulay tensor products. In these earlier results, we replace $^{e}R$ with a more general module $^{e}M$, where $R$ is a Cohen-Macaulay ring, $M$ is a Cohen-Macaulay $R$-module with full support, and $^{e}M$ is the module viewed as an $R$-module via the $e$-th iteration of the Frobenius endomorphism. We also provide examples and present applications of our results, yielding new characterizations of the regularity of local rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15048 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the test properties of the Frobenius endomorphism Celikbas, Olgur Sadeghi, Arash Yao, Yongwei Commutative Algebra In this paper, we prove two theorems concerning the test properties of the Frobenius endomorphism over commutative Noetherian local rings of prime characteristic $p$. Our first theorem generalizes a result of Funk-Marley on the vanishing of Ext and Tor modules, while our second theorem generalizes one of our previous results on maximal Cohen-Macaulay tensor products. In these earlier results, we replace $^{e}R$ with a more general module $^{e}M$, where $R$ is a Cohen-Macaulay ring, $M$ is a Cohen-Macaulay $R$-module with full support, and $^{e}M$ is the module viewed as an $R$-module via the $e$-th iteration of the Frobenius endomorphism. We also provide examples and present applications of our results, yielding new characterizations of the regularity of local rings. |
| title | On the test properties of the Frobenius endomorphism |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2502.15048 |