Huybrechts' K3 surfaces Hodge–motive–L-equivalence conjecture

Let $S$ and $S'$ be complex projective K3 surfaces. Write $H^2(S,\mathbb{Q})\cong H^2(S',\mathbb{Q})$ for an isomorphism of rational Hodge structures, $\mathfrak h(S)\cong\mathfrak h(S')$ for an isomorphism of rational Chow motives, and let $K_0(\operatorname{Var}_{\mathbb{C}})[\mathbb{L}^{-1}]$ denote the localization of the Grothendieck ring of complex varieties by the affine-line class $\mathbb{L}$. Huybrechts' conjecture. The following conditions are equivalent: (i) $H^2(S,\mathbb{Q})\cong H^2(S',\mathbb{Q})$; (ii) $\mathfrak h(S)\cong\mathfrak h(S')$; (iii) $[S]=[S']$ in an appropriate localization of $K_0(\operatorname{Var}_{\mathbb{C}})[\mathbb{L}^{-1}]$. The paper states that this is the original version of Huybrechts' conjecture and that it is disproved there; the published version was modified.