The monomorphism category of Gorenstein projective modules and comparision with the category of matrix factorization
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911904266452992 |
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| author | Bahlekeh, Abdolnaser Fotouhi, Fahimeh Sadat Nateghi, Armin Salarian, Shokrollah |
| author_facet | Bahlekeh, Abdolnaser Fotouhi, Fahimeh Sadat Nateghi, Armin Salarian, Shokrollah |
| contents | Let ($S, \mathfrak{n})$ be a commutative noetherian local ring and let $ω\in\mathfrak{n}$ be non-zero divisor. This paper is concerned with the category of monomorphisms between finitely generated Gorenstein projective S-modules, such that their cokernels are annihilated by $ω$. We will observe that this category, which will be denoted by Mon$(ω,\mathcal{G})$, is an exact category in the sense of Quillen. More generally, it is proved that Mon$(ω,\mathcal{G})$ is a Frobenius category. Surprisingly, it is shown that not only the category of matrix factorizations embeds into Mon$(ω,\mathcal{G})$, but also its stable category as well as the singularity category of the factor ring $R = S/(ω)$, can be realized as triangulated subcategories of the stable category of Mon$(ω,\mathcal{G})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13833 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The monomorphism category of Gorenstein projective modules and comparision with the category of matrix factorization Bahlekeh, Abdolnaser Fotouhi, Fahimeh Sadat Nateghi, Armin Salarian, Shokrollah Representation Theory Let ($S, \mathfrak{n})$ be a commutative noetherian local ring and let $ω\in\mathfrak{n}$ be non-zero divisor. This paper is concerned with the category of monomorphisms between finitely generated Gorenstein projective S-modules, such that their cokernels are annihilated by $ω$. We will observe that this category, which will be denoted by Mon$(ω,\mathcal{G})$, is an exact category in the sense of Quillen. More generally, it is proved that Mon$(ω,\mathcal{G})$ is a Frobenius category. Surprisingly, it is shown that not only the category of matrix factorizations embeds into Mon$(ω,\mathcal{G})$, but also its stable category as well as the singularity category of the factor ring $R = S/(ω)$, can be realized as triangulated subcategories of the stable category of Mon$(ω,\mathcal{G})$. |
| title | The monomorphism category of Gorenstein projective modules and comparision with the category of matrix factorization |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2402.13833 |