  In underdoped cuprates fluctuations of the phase of the superconducting order
parameter play a role due to the small superfluid density. We consider the
effects of phase fluctuations assuming the exchange of spin fluctuations to be
the predominant pairing interaction. Spin fluctuations are treated in the
fluctuation-exchange approximation, while phase fluctuations are included by
Berezinskii-Kosterlitz-Thouless theory. We calculate the stiffness against
phase fluctuations, ns(omega)/m*, as a function of doping, temperature, and
frequency, taking its renormalization by phase fluctuations into account. The
results are compared with recent measurements of the high-frequency
conductivity. Furthermore, we obtain the temperature T*, where the density of
states at the Fermi energy starts to be suppressed, the temperature Tc*, where
Cooper pairs form, and the superconducting transition temperature Tc, where
their phase becomes coherent. We find a crossover from a
phase-fluctuation-dominated regime with Tc proportinal to ns for underdoped
cuprates to a BCS-like regime for overdoped materials.
