On Amiot's conjecture

Abstract

In a survey paper in 2011, Amiot proposed a conjectural characterisation of the cluster categories which were conceived in the mid 2000s to lift the combinatorics of Fomin-Zelevinsky's cluster algebras to the categorical level. This paper is devoted to a proof of (a variant of) her conjecture. More generally, cluster categories admit higher-dimensional and relative variants, the so-called Higgs categories recently introduced by Wu. We also prove higher-dimensional and relative variants of the conjecture.

43 pages. arXiv admin note: text overlap with arXiv:2307.16222; v2: extended definition of right CY structures to homologically finite dg algebras; v3: main results extended to the 1-dimensional case