Removal of torsion hypotheses in the Ext and Tor regularity theorem

Determine whether the conclusion of Theorem 3.5 for the eventual regularity of \(\Ext_R^k(L,M/\mathbf{I}^{\underline n}N)\) and \(\Tor_k^R(L,M/\mathbf{I}^{\underline n}N)\) remains valid without assuming that \(\Ext_R^k(L,M)\) or \(\Tor_k^R(L,M)\) is \(R_+\)-torsion, or that the corresponding modules \(\Ext_R^k(L,M/\mathbf{I}^{\underline n}N)\) or \(\Tor_k^R(L,M/\mathbf{I}^{\underline n}N)\) are \(R_+\)-torsion for all sufficiently large \(\underline n\).

Background

Theorem 3.5 proves, under an $R_+$-torsion assumption on either the limiting Ext or Tor module or the asymptotic family, that the family is eventually zero or nonzero and that its regularity is either eventually constant at the regularity of the limiting module or eventually the supremum of finitely many linear functions.

The authors explicitly ask whether these conclusions persist without either of the two torsion conditions.