Tilting complexes and codimension functions over commutative noetherian rings
Abstract
In the derived category of a commutative noetherian ring, we explicitly construct a silting object associated with each sp-filtration of the Zariski spectrum satisfying the "slice" condition. Our new construction is based on local cohomology and it allows us to study when the silting object is tilting. For a ring admitting a dualizing complex, this occurs precisely when the sp-filtration arises from a codimension function on the spectrum. In the absence of a dualizing complex, the situation is more delicate and the tilting property is closely related to the condition that the ring is a homomorphic image of a Cohen-Macaulay ring. We also provide dual versions of our results in the cosilting case.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2022
- DOI:
- 10.48550/arXiv.2207.01309
- arXiv:
- arXiv:2207.01309
- Bibcode:
- 2022arXiv220701309H
- Keywords:
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- Mathematics - Commutative Algebra;
- Mathematics - Rings and Algebras;
- Mathematics - Representation Theory;
- 13D09 (Primary) 13D45;
- 13H10;
- 18G80 (Secondary)
- E-Print:
- 64 pages, minor revision