The monomorphism category of Gorenstein projective modules and comparision with the category of matrix factorization
| Autor: | Bahlekeh, Abdolnaser, Fotouhi, Fahimeh Sadat, Nateghi, Armin, Salarian, Shokrollah |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let ($S, \mathfrak{n})$ be a commutative noetherian local ring and let $\omega\in\mathfrak{n}$ 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 $\omega$. We will observe that this category, which will be denoted by Mon$(\omega,\mathcal{G})$, is an exact category in the sense of Quillen. More generally, it is proved that Mon$(\omega,\mathcal{G})$ is a Frobenius category. Surprisingly, it is shown that not only the category of matrix factorizations embeds into Mon$(\omega,\mathcal{G})$, but also its stable category as well as the singularity category of the factor ring $R = S/(\omega)$, can be realized as triangulated subcategories of the stable category of Mon$(\omega,\mathcal{G})$. Comment: Section 3 of the paper has been completely modified. Also some modifications in Section 2 have been made. The title and abstract also changed |
| Databáze: | arXiv |
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