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Christensen, Lars Winther; Iyengar, Srikanth B.; Marley, Thomas
Proceedings of the Edinburgh Mathematical Society, 05/2019, Letnik: 62, Številka: 2Journal Article
Let be a prime ideal in a commutative noetherian ring R. It is proved that if an R-module M satisfies ${\rm Tor}_n^R $(k ( ), M) = 0 for some n ⩾ R , where k( ) is the residue field at , then ${\rm Tor}_i^R $(k ( ), M) = 0 holds for all i ⩾ n. Similar rigidity results concerning ${\rm Tor}_R^{\ast} $(k ( ), M) are proved, and applications to the theory of homological dimensions are explored.
