Rigidity of Ext and Tor with coefficients in residue fields of a commutative noetherian ring
Commutative Algebra
2017-07-31 v2
Abstract
Let p be a prime ideal in a commutative noetherian ring R. It is proved that if an R-module M satisfies Tor^R_n(k(p),M) = 0 for some n \geq dim R_p, where k(p) is the residue field at p, then Tor^R_i(k(p),M) = 0 holds for all i \geq n. Similar rigidity results concerning Ext_R^*(k(p),M) are proved, and applications to the theory of homological dimensions are explored.
Keywords
Cite
@article{arxiv.1611.03280,
title = {Rigidity of Ext and Tor with coefficients in residue fields of a commutative noetherian ring},
author = {Lars Winther Christensen and Srikanth B. Iyengar and Thomas Marley},
journal= {arXiv preprint arXiv:1611.03280},
year = {2017}
}
Comments
Final version, to appear in Proc. Edinb. Math. Soc.; 15 pp