  We consider the Fermi surface inside the antiferromagnetic ordered region of
a Kondo lattice system in an arbitrary dimension higher than one. We establish
the existence of ${\rm AF_S}$, an antiferromagnetic phase whose Fermi surface
is ``small,'' in the sense that the local moments do not participate in the
Fermi-surface formation. This is in contrast to the ``large'' Fermi surface
that is typically assumed for heavy fermion metals. We extend our earlier work
to the case that the Fermi surface of the conduction electrons intersects the
antiferromagnetic Brillouin zone boundary. Our results provide a new
perspective on local quantum criticality. In addition, our results imply that,
for the ${\rm AF_S}$ phase, it is important to keep track of the dynamical
screening processes; we suggest that this effect is not captured in a recent
variational Monte-Carlo study of the Kondo lattice.
