  We discuss a conjecture saying that derived equivalence of simply connected
smooth projective varieties implies that the difference of their classes in the
Grothendieck ring of varieties is annihilated by a power of the affine line
class.
  We support the conjecture with a number of known examples, and one new
example. We consider a smooth complete intersection $X$ of three quadrics in
${\mathbf P}^5$ and the corresponding double cover $Y \to {\mathbf P}^2$
branched over a sextic curve. We show that as soon as the natural Brauer class
on $Y$ vanishes, so that $X$ and $Y$ are derived equivalent, the difference
$[X] - [Y]$ is annihilated by the affine line class.
