Amiot's conjecture on quivers with potential

Establish that every algebraic 2-Calabi–Yau triangulated category over an algebraically closed field of characteristic zero possessing a 2-cluster tilting object is triangle equivalent to the cluster category associated with a Jacobi-finite quiver with potential.

Background

The paper recalls Amiot's conjecture as a converse to the generalized cluster-category construction. It concerns algebraic 2-Calabi–Yau triangulated categories equipped with a 2-cluster tilting object and asks whether every such category arises from a Jacobi-finite quiver with potential.

The paper notes that Keller–Liu proved the conjecture under the additional assumption of a pseudo-compact enhancement. Consequently, the unrestricted formulation stated here remains the explicitly identified conjectural problem, whereas the paper proves a different intrinsic dg-categorical variant that does not provide the additional quiver-with-potential normal form.

References

The following question of Amiot Question~2.20 is now known as Amiot's conjecture.

\begin{Conj}[Amiot's conjecture] Let $k$ be an algebraically closed field with $\ch k=0$. Let $C$ be an algebraic $2$-Calabi--Yau triangulated category with a $2$-cluster tilting object. Then there exists a Jacobi-finite quiver with potential $(Q,W)$ such that $C\simeqC_{Q,W}$ holds. \end{Conj}

— Auslander correspondence for higher stable dg categories and cluster Morita theory  (2608.30740 - Tomonaga, 31 Aug 2026) in Section 3, “Applications to Amiot's conjecture,” Conjecture (Amiot's conjecture)