Rigidity of Ext and Tor via flat–cotorsion theory
LW Christensen, L Ferraro… - Proceedings of the …, 2023 - cambridge.org
Let. 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.
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.
Rigidity of Ext and Tor via flat-cotorsion theory
L Winther Christensen, L Ferraro… - arXiv e-prints, 2021 - ui.adsabs.harvard.edu
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.
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.
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