  Let $X$ be a hyperk\"ahler variety. Beauville has conjectured that a certain
subring of the Chow ring of $X$ should inject into cohomology. This note
proposes a similar conjecture for the ring of algebraic cycles on $X$ modulo
algebraic equivalence: a certain subring (containing divisors and codimension
$2$ cycles) should inject into cohomology. We present some evidence for this
conjecture.

Algebraic Geometry