The Iwanaga–Gorenstein Wakamatsu tilting conjecture

Let $\Lambda$ be an Iwanaga–Gorenstein artin algebra. A module is Wakamatsu tilting if it satisfies the Wakamatsu tilting conditions, and tilting if it has finite projective dimension, is self-orthogonal, and has the required number of indecomposable summands.

Iwanaga–Gorenstein Wakamatsu tilting conjecture. Any Wakamatsu tilting $\Lambda$-module is tilting.

The conjecture would extend the equivalence between tilting, projectively Wakamatsu tilting, and Wakamatsu tilting modules established in the representation-finite Iwanaga–Gorenstein case. The paper observes that it follows from the Wakamatsu tilting conjecture.