Context. Pressure maxima are regions in protoplanetary disks in which pebbles can be trapped because the regions have no local pressure gradient. These regions could be ideal places in which planetesimals might be formed or to isotopic reservoirs might be isolated. Observations of protoplanetary disks show that dusty ring structures are common, and pressure maxima are sometimes 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 that are identified among chondrites and iron meteorites. In this paper, we detail a mechanism by which pressure maxima form just inward of the snow line in stratified disks (with a dead zone and an active layer). This mechanism does not require the presence of a planet.Aims. We investigate the conditions for the formation of pressure maxima using a vertically averaged α viscosity model and release of water vapor at the snow line.Methods. We considered a 1D α disk model. Using a combination of analytical and numerical investigations, we explored the range of conditions for a pressure maximum to form inside the dead zone and just inward of the snow line.Results. When the vertically averaged α is a decreasing function of the surface density, then the release of water vapor at the snow line decreases the sound velocity, and a pressure bump appears in turn. This requires a constant inflow of icy pebbles with a ratio of the pebble influx to gas influx >0.6 for a power-law disk with a 1% ice-to-gas ratio, and >1.8 for a disk with an ice-to-gas ratio ~0.3%. If these conditions are met, then a pressure maximum appears just inward of the snow line due to a process that couples 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 decrease in sound velocity inward of the snow line through the release of water vapor.Conclusions. This mechanism is promising for isolating early reservoirs carrying different isotopic signatures in the Solar System and for promoting dry planetesimal formation inward of the snow line, provided the vertically averaged description of a dead zone is valid.