English

Cotorsion pairs and Tor-pairs over commutative noetherian rings

Commutative Algebra 2024-11-08 v1 Rings and Algebras

Abstract

For a commutative noetherian ring RR, 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