Beauville–Voisin conjecture for hyperkähler varieties

Let $T$ be a hyperkähler variety. Write $\operatorname{CH}^1(T)$ for the divisor classes, $c_i(T)$ for the Chern classes of $T$, and $\mathrm{cl}$ for the cycle class map. Beauville–Voisin conjecture. The cycle class map restricted to the subring generated by divisors and Chern classes,

$$\mathrm{cl}\colon\left\langle\operatorname{CH}^1(T), c_i(T)\right\rangle\to H^\ast(T,\mathbb{Q}),$$

is injective. The conjecture extends Beauville's divisor-generation conjecture by including Chern classes; the source records cases already proved, including generalised Kummer varieties, double EPW sextics, and some other deformation types.