Weak proregularity, weak stability, and the noncommutative MGM equivalence

We then study weak stability of torsion classes in module categories over noncommutative rings. There are three main theorems in this context: ▷ For a torsion class T that is weakly stable, quasi-compact and finite dimensional, the right derived torsion functor is isomorphic to a left derived tensor functor. ▷ The Noncommutative MGM Equivalence, that holds under the same assumptions on T. ▷ A theorem about symmetric derived torsion for complexes of bimodules. This last theorem is a generalization of a result of Van den Bergh from 1997, and corrects an error in a paper of Yekutieli & Zhang from 2003.