  We present a theoretical study of the influence of dephasing on shot noise in
an electronic Mach-Zehnder interferometer. In contrast to phenomenological
approaches, we employ a microscopic model where dephasing is induced by the
fluctuations of a classical potential. This enables us to treat the influence
of the environment's fluctuation spectrum on the shot noise. We compare against
the results obtained from a simple classical model of incoherent transport, as
well as those derived from the phenomenological dephasing terminal approach,
arguing that the latter runs into a problem when applied to shot noise
calculations for interferometer geometries. From our model, we find two
different limiting regimes: If the fluctuations are slow as compared to the
time-scales set by voltage and temperature, the usual partition noise
expression T(1-T) is averaged over the fluctuating phase difference. For the
case of ``fast'' fluctuations, it is replaced by a more complicated expression
involving an average over transmission amplitudes. The full current noise also
contains other contributions, and we provide a general formula, as well as
explicit expressions and plots for specific examples.
