Rigidity of Ext and Tor via flat-cotorsion theory
Commutative Algebra
2023-09-20 v2
Abstract
Let p be a prime ideal in a commutative noetherian ring R and denote by k(p) the residue field of the local ring R_p. We prove that if an R-module M satisfies Ext_R^n(k(p),M) = 0 for some n >= dim R, then Ext_R^i(k(p),M) = 0 holds for all i >= n. This improves a result of Christensen, Iyengar, and Marley by lowering the bound on n. We also improve existing results on Tor-rigidity. This progress is driven by the existence of minimal semi-flat-cotorsion replacements in the derived category as recently proved by Nakamura and Thompson.
Cite
@article{arxiv.2112.00103,
title = {Rigidity of Ext and Tor via flat-cotorsion theory},
author = {Lars Winther Christensen and Luigi Ferraro and Peder Thompson},
journal= {arXiv preprint arXiv:2112.00103},
year = {2023}
}
Comments
Final version, to appear in Proc. Edinb. Math. Soc.; 10 pp