Rigidity of Ext and Tor via flat–cotorsion theory

Authors

Lars Winther Christensen
Luigi Ferraro, The University of Texas Rio Grande Valley
Peder Thompson

Document Type

Article

Publication Date

11-3-2023

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.

Comments

Original published version available at https://doi.org/10.1017/S0013091523000573

Recommended Citation

Christensen, Lars Winther, Luigi Ferraro, and Peder Thompson. "Rigidity of ext and tor via flat–cotorsion theory." Proceedings of the Edinburgh Mathematical Society 66, no. 4 (2023): 1142-1153. https://doi.org/10.1017/S0013091523000573

Publication Title

Proceedings of the Edinburgh Mathematical Society

DOI

10.1017/S0013091523000573