Beauville's injectivity conjecture for the divisor-generated Chow subalgebra

Let $X$ be a projective hyperkähler manifold, and let $A^{*}(X)$ denote its Chow ring. The cycle class map is the map

$$cl:A^{*}(X)\longrightarrow H^{*}(X).$$

Beauville's conjecture. The cycle class map is injective on the subalgebra of $A^{*}(X)$ generated by divisors.

This conjecture concerns the relationship between algebraic cycles and cohomology on hyperkähler manifolds. The source recalls that the cycle class map has an infinite-dimensional kernel in top codimension, while Beauville's conjecture predicts injectivity for the much smaller subalgebra generated by divisor classes.