Tests of the locality of exact Kohn-Sham exchange potentials

It is commonly assumed that exact Kohn-Sham theory implies a local exchange-correlation potential for ground states. Here we show that this is not true for the exchange potential in a Hartree-Fock model of density-functional theory, although Hohenberg-Kohn theorems can be proved for this model. It may not be possible to express exact Kohn-Sham equations in general in terms of density-functional derivatives that are equivalent to local potential functions.