Kuznetsov's rationality conjecture for cubic fourfolds

Claims that for every sufficiently large admissible Hassett discriminant $d$ a very general cubic fourfold of discriminant $d$ is irrational although its Kuznetsov component is the derived category of a K3 surface and it has an associated polarized K3 in Hassett's Hodge-theoretic sense. This disproves Kuznetsov's conjecture and the sufficiency of the associated-K3 criterion (and of Fano variety birational to a K3 Hilbert square). The threshold is ineffective; no specific discriminant is shown irrational, the necessity direction is untouched, and stable rationality is not decided. These are not the first irrational cubic fourfolds: the paper cites Katzarkov-Kontsevich-Pantev-Yu (very general cubic) and Fay (some special divisors).

Claims that for every sufficiently large admissible Hassett discriminant $d$ a very general cubic fourfold of discriminant $d$ is irrational although its Kuznetsov component is the derived category of a K3 surface and it has an associated polarized K3 in Hassett's Hodge-theoretic sense. This disproves Kuznetsov's conjecture and the sufficiency of the associated-K3 criterion (and of Fano variety birational to a K3 Hilbert square). The threshold is ineffective; no specific discriminant is shown irrational, the necessity direction is untouched, and stable rationality is not decided. These are not the first irrational cubic fourfolds: the paper cites Katzarkov-Kontsevich-Pantev-Yu (very general cubic) and Fay (some special divisors).