  We present a study of the Nernst effect in amorphous 2D superconductor
InO$_x$, whose low carrier density implies low phase rigidity and strong
superconducting phase fluctuations. Instead of presenting the abrupt jump
expected at a BCS transition, the Nernst signal evolves continuously through
the superconducting transition as previously observed in underdoped cuprates.
This contrasts with the case of Nb$_{0.15}$Si$_{0.85}$, where the Nernst signal
due to vortices below T$_{c}$ and by Gaussian fluctuations above are clearly
distinct. The behavior of the ghost critical field in InO$_x$ points to a
correlation length which does not diverge at $T_c$, a temperature below which
the amplitude fluctuations freeze, but phase fluctuations survive.
