The Kuznetsov rationality conjecture for cubic fourfolds asserts that a smooth complex cubic fourfold is
rational precisely when its Kuznetsov component
is exactly 
-linearly equivalent to the ordinary bounded derived
category of a smooth projective K3 surface. The
target category in this formulation has no Brauer twisting.
For a discriminant 
, the Hassett divisor 
parametrizes smooth cubic
fourfolds whose integral 
-cohomology contains a saturated
positive-definite rank-two sublattice containing 
and having determinant 
, where 
. The admissible discriminants satisfy
 |
and no odd prime congruent to 2 modulo 3 divides 
.
For instance, 14 and 26 meet these arithmetic conditions.
