A pump module, a pump base module and a pump system in which the pump module has a base and a flexibly deformable membrane, with the base and the membrane forming a line-shaped pump channel that is curved at least in sections, and the base having a pump channel inlet and a pump channel outlet, wherein the pump channel inlet and the pump channel outlet are connected with the pump channel for supplying and discharging a fluid in the pump channel in such a way, so that through a periodically rotating deformation of the membrane a fluid can be pumped through the pump channel from the pump channel inlet to the pump outlet.