The ever-increasing number of computation units assembled in current HPC platforms leads to a concerning increase in fault probability. Traditional checkpoint/restart strategies avoid wasting large amounts of computation time when such fault occurs. With the increasing amount of data dealt with by current applications, these strategies however suffer from their data transfer demand becoming unreasonable, or the entailed global synchronizations. Meanwhile, the current trend towards task-based programming is an opportunity to revisit the principles of the checkpoint/restart strategies. We here propose a checkpointing scheme which is closely tied to the execution of task graphs. We describe how it allows for completely asynchronous and distributed checkpointing, as well as localized node restart, thus opening up for very large scalability. We also show how a synergy between the application data transfers and the checkpointing transfers can lead to a reasonable additional network load, measured to be lower than +10% on a dense linear algebra example.