Product-complete tilting complexes and Cohen-Macaulay hearts

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00600360" target="_blank" >RIV/67985840:_____/24:00600360 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4171/rmi/1500" target="_blank" >https://doi.org/10.4171/rmi/1500</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/RMI/1500" target="_blank" >10.4171/RMI/1500</a>

Result language
angličtina
Original language name
Product-complete tilting complexes and Cohen-Macaulay hearts
Original language description
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 Dbfg(R) ≃ Db(B)op between mod-R 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 Dbfg(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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA23-05148S" target="_blank" >GA23-05148S: Homological and structural theory in geometric contexts</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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