Abrupt variations in asset prices or returns have important consequences in the financial market, and may imply significant gains or losses. Modeling jumps in financial series is, therefore, useful in risk assessment or asset pricing. Hawkes processes, on the other hand, allow us to represent phenomena whose occurrence of an event stimulates the occurrence of new events in subsequent moments. If we assume the possibility that abrupt variations in asset prices or returns can induce new variations of large magnitude at later times, then Hawkes processes can serve as an alternative to the usual Poisson processes in modeling jumps in financial series. In this article we consider series of some of the main cryptocurrencies, minute by minute, from September 2021 to July 2022. The results indicate that, in this market, the Hawkes process outperforms the Poisson process. They also help to better understand the dynamics of this cryptocurrency market and, therefore, have relevant implications for the decisions of investors and risk managers.