  We study the quantum critical behavior in an isotropic Fermi liquid in the
vicinity of a zero-temperature density-wave transition at a finite wave vector
q_c. We show that, near the transition, the Landau damping of the soft bosonic
mode yields a crossover in the fermionic self-energy from Sigma(k,omega) ~
Sigma(k) to Sigma(k,omega) ~ Sigma(omega), where k and omega are momentum and
frequency. Because of this self-generated locality, the fermionic effective
mass diverges right at the quantum critical point, not before, i.e., the Fermi
liquid survives up to the critical point.
