The self-orthogonal module conjecture for Iwanaga–Gorenstein algebras

Let $\Lambda$ be an Iwanaga–Gorenstein artin algebra, meaning that $\operatorname{id}\Lambda_\Lambda$ and $\operatorname{pd}(D\Lambda)_\Lambda$ are finite. A $\Lambda$-module $T$ is self-orthogonal if $\operatorname{Ext}^i_\Lambda(T,T)=0$ for every $i>0$.

Self-orthogonal module conjecture. Every self-orthogonal $\Lambda$-module has finite projective dimension.

The conjecture extends the result proved in the paper for representation-finite Iwanaga–Gorenstein algebras to the representation-infinite case. Its self-injective special case is the Tachikawa conjecture.