Equality of twisted and classical Beauville–Voisin classes on K3 surfaces

Establish that the twisted Beauville–Voisin zero-cycle class o_{𝒳} ∈ CH_0(X), constructed for a μ_m-gerbe twist p: 𝒳 → X of a K3 surface X, coincides with the classical Beauville–Voisin class o_X ∈ CH_0(X) for every twist; that is, prove o_{𝒳} = o_X for all 𝒳 → X.

Background

The paper constructs a twisted Beauville–Voisin class o_{𝒳} in CH_0(X) for twisted K3 surfaces, generalizing results by O’Grady and Shen–Yin–Zhao to the twisted setting. When the twist is essentially trivial, the construction recovers the usual Beauville–Voisin class o_X. The authors provide evidence via Bloch–Beilinson heuristics that o_{𝒳} should agree with o_X more generally, but a proof is not given.

This conjecture asks for a full identification of the twisted class with the classical Beauville–Voisin class across all twists, thereby upgrading the filtered and derived invariance properties proved in the paper to an exact identification of canonical zero-cycle representatives.