The stable category of monomorphisms between (Gorenstein) projective modules with applications
| Autor: | Bahlekeh, Abdolnaser, Fotouhi, Fahimeh Sadat, Hamlehdari, Mohammad Amin, Salarian, Shokrollah |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1515/forum-2023-0317 |
| Popis: | Let (S; n) be a commutative noetherian local ring and let w in n be non-zero divisor. This paper is concerned with the two categories of monomorphisms between finitely generated (Gorenstein) projective S-modules, such that their cokernels are annihilated by w. It is shown that these categories, which will be denoted by Mon(w;P) and Mon(w; G), are both Frobenius categories with the same projective objects. It is also proved that the stable category Mon(w;P) is triangle equivalent to the category of D-branes of type B, DB(w), which has been introduced by Kontsevich and studied by Orlov. Moreover, it will be observed that the stable categories Mon(w;P) and Mon(w; G) are closely related to the singularity category of the factor ring R = S/(w). Precisely, there is a fully faithful triangle functor from the stable category Mon(w; G) to Dsg(R), which is dense if and only if R (and so S) are Gorenstein rings. Particularly, it is proved that the density of the restriction of this functor to Mon(w;P), guarantees the regularity of the ring S. Comment: to appear in Forum Mathematicum |
| Databáze: | arXiv |
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