Brick Brauer–Thrall II' conjecture

Let $\Lambda$ be a finite-dimensional algebra. A module $M\in\operatorname{mod}\Lambda$ is a brick if $\operatorname{End}_{\Lambda}(M)$ is a division algebra. The algebra $\Lambda$ is $\tau$-tilting infinite if it has infinitely many isomorphism classes of basic $2$-term silting complexes. Brick Brauer–Thrall II' conjecture. If $\Lambda$ is $\tau$-tilting infinite, then there exists a dimension vector $\mathbf d$ such that there are infinitely many isomorphism classes of bricks $M\in\operatorname{mod}\Lambda$ of dimension vector $\mathbf d$. This is also known as the $\tau$-Brauer–Thrall II' conjecture and is weaker than Pfeifer's stable version, which additionally requires a common stability parameter; its general status is not resolved in the supplied text.