Product-complete tilting complexes and Cohen–Macaulay hearts
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Michal Hrbek [1] ; Lorenzo Martini [2]
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[1] Czech Academy of Sciences, Prague, Czech Republic
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[2] Università di Verona, Verona, Italy
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- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 6, 2024, págs. 2339-2369
- Idioma: inglés
- DOI: 10.4171/RMI/1500
- Enlaces
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Resumen
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)<∞, we show that there is a derived duality D fg b (R)≅D b(B) op between modR and a noetherian abelian category 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 D fg b (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.
