  We define and study the invariance properties of homological units. Some
applications are given to the derived invariance of Hodge numbers. In
particular, we prove that if X and Y are derived equivalent smooth projective
varieties of dimension 4 having the same Picard number, then they have the same
Hodge numbers. We also give a geometric interpretation of the conjectural
invariance of homological units in terms of derived Jacobians.
