TY - UNPB
T1 - Cotorsion pairs and Tor-pairs over commutative noetherian rings
AU - Herbera, Dolors
AU - Hrbek, Michal
AU - Gros, Giovanna Le
N1 - 27 pages
PY - 2024/11/7
Y1 - 2024/11/7
N2 - 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.
AB - 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.
KW - math.AC
KW - math.RA
KW - 13D07, 13C15, 13E05 (Prymary) 13C11, 16E30 (Secondary)
UR - https://portalrecerca.uab.cat/en/publications/523cda0f-0efe-4cac-a2cf-5c8d34200332
U2 - 10.48550/arXiv.2411.04514
DO - 10.48550/arXiv.2411.04514
M3 - Preprint
BT - Cotorsion pairs and Tor-pairs over commutative noetherian rings
ER -