  We present a complete computation of the inflaton decay into very massive
fermions during preheating. We show that heavy fermions are produced very
efficiently up to masses of order 10^{17}-10^{18} GeV; the accessible mass
range is thus even broader than the one for heavy bosons. We apply our findings
to the leptogenesis scenario, proposing a new version of it, in which the
massive right-handed neutrinos, responsible for the generation of the baryon
asymmetry, are produced during preheating. We also discuss other production
mechanisms of right-handed neutrinos in the early Universe, identifying the
neutrino mass parameters for which the observed baryon asymmetry is reproduced.
