  Pressure maxima are regions in protoplanetary disks where pebbles can be
trapped because of the local absence of pressure gradient. These regions could
be ideal places to form planetesimals or to isolate isotopic reservoirs.
Observations of protoplanetary disks show that dusty rings structures are
common, and pressure maxima are sometime invoked as a possible explanation. In
our Solar System, pressure bumps have been suggested as a possible mechanism
for separating reservoirs with different nucleosynthetic compositions. In this
letter we detail a mechanism by which pressure maxima form just inward the
snow-line in stratified disks. This mechanism does not need the presence of a
planet. Using a combination of analytical and numerical investigation we
explore the range of conditions for a pressure maximum to form inside the
dead-zone and just inward the snow-line. When the vertically averaged $\alpha$
is a decreasing function of surface density then the release of water vapor at
the snow-line lowers the sound velocity, and in turn, a pressure bump appears.
This requires a constant inflow of icy pebbles with pebbles influx to gas
influx $>0.6$ for a power law disk with $1\%$ ice/gas ratio, and $>1.8$ for a
disk with ice/gas ratio $\sim 0.3\%$. If these conditions are met, then a
Pressure-maximum appears just inward the snow-line due to a process coupling
the dead and active layers at the evaporation front. The pressure bump survives
as long as the icy pebble flux is high enough. The formation of the pressure
bump is triggered by the drop of sound velocity inward the snow-line, due to
the release of water vapor. This mechanism is promising for isolating early
reservoirs carrying different isotopic signatures in the Solar System and for
promoting dry planetesimal formation inward the snow-line, provided the
vertically averaged description of a dead-zone is valid.
