Cotorsion pairs and Tor-pairs over commutative noetherian rings
Commutative Algebra
2024-11-08 v1 Rings and Algebras
Abstract
For a commutative noetherian ring , we classify all the hereditary cotorsion pairs cogenerated by pure-injective modules of finite injective dimension. The classification is done in terms of integer-valued functions on the spectrum of the ring. Each such function gives rise to a system of local depth conditions which describes the left-hand class in the corresponding cotorsion pair. Furthermore, we show that these cotorsion pairs correspond by explicit duality to hereditary Tor-pairs generated by modules of finite flat dimension.
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Cite
@article{arxiv.2411.04514,
title = {Cotorsion pairs and Tor-pairs over commutative noetherian rings},
author = {Dolors Herbera and Michal Hrbek and Giovanna Le Gros},
journal= {arXiv preprint arXiv:2411.04514},
year = {2024}
}
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27 pages