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arXiv · 2411.04514

Cotorsion pairs and Tor-pairs over commutative noetherian rings

Dolors Herbera·Michal Hrbek·Giovanna Le Gros
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Abstract

For a commutative noetherian ring $R$, 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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Dolors Herbera, Michal Hrbek, Giovanna Le Gros. 2024-11-07. Cotorsion pairs and Tor-pairs over commutative noetherian rings. https://arxiv.org/abs/2411.04514

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