  We give a local integral formula, valid on general curved space-times, for
the characteristic Cauchy problem for the Dirac equation with arbitrary spin
using the method developed by Friedlander in his book "the wave equation on a
curved spacetime" (1975). The results obtained by Penrose in the flat case in
"Null hypersurface initial data for classical fields of arbitrary spin for
general relativity" (Gen. Rel. Grav 1980) are recovered directly. It is
expected that this method can be used to obtain sharp estimates for the
characteristic Cauchy problem for the Dirac equation.
