  A L\'evy processes resurrected in the positive half-line is a Markov process
obtained by removing successively all jumps that make it negative. A natural
question, given this construction, is whether the resulting process is absorbed
at 0 or not. We first describe the law of the resurrected process in terms of
that of the initial L\'evy process. Then in many important classes of L\'evy
processes, we give conditions for absorption and conditions for non absorption
bearing on the characteristics of the initial L\'evy process.
