  We show that in SU(2) Yang-Mills theories a simple relation exists between
lattice gluon propagators in Coulomb and Landau gauge and discuss the physical
implications of such result. In particular, the realization of the
Gribov-Zwanziger confinement mechanism in Coulomb gauge, linked to
dual-superconductivity, would imply that the standard BRST charge must be ill
defined non perturbatively. As a consequence, the Kugo-Ojima confinement
criterion, which relies on BRST charge conservation beyond perturbation theory,
would not be fulfilled.
