Product-complete tilting complexes and Cohen-Macaulay hearts
| Autor: | Hrbek, Michal, Martini, Lorenzo |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We show that the cotilting heart associated to a tilting complex $T$ is a locally coherent and locally coperfect Grothendieck category (i.e. an Ind-completion of a small artinian abelian category) if and only if $T$ is product-complete. We then apply this to the specific setting of the derived category of a commutative noetherian ring $R$. If $\dim(R)<\infty$, we show that there is a derived duality $\mathcal{D}^b_{fg}(R) \cong \mathcal{D}^b(\mathcal{B})^{op}$ between $\mathrm{mod} R$ and a noetherian abelian category $\mathcal{B}$ if and only if $R$ is a homomorphic image of a Cohen--Macaulay ring. Along the way, we obtain new insights about t-structures in $\mathcal{D}^b_{fg}(R)$. In the final part, we apply our results to obtain a new characterization of the class of those finite-dimensional Noetherian rings that admit a Gorenstein complex. Comment: 27 pages, third version, to appear in Revista Matem\'atica Iberoamericana |
| Databáze: | arXiv |
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