Big finitistic dimension of finite dimensional algebra

Let $$A$$ be a finite dimensional algebra. The big finitistic dimension of $$A$$ is

$$\operatorname{FinDim}(A)=\sup\{\operatorname{pd}(M)\mid M\in \text{Mod-}A \text{ and } \operatorname{pd}(M)<\infty\},$$ where $$\operatorname{pd}(M)$$ is the projective dimension of $$M$$, $$\text{Mod-}A$$ is the category of right $$A$$-modules.

Problem: Does there exist a finite dimensional algebra $$A$$ such that $$\operatorname{FinDim}(A)=\infty?$$

http://cn.arxiv.org/abs/1804.09801 (see Definition 4.1.)

• A more interesting question (although not very mathematical) would be whether one thinks that the conjecture is true. I think it is false. The opinion seems to be roughly split 50-50 on true-false when I asked several people working on it. – Mare Oct 9 '18 at 12:32