  We study the peeling of Dirac and Maxwell fields on a Schwarzschild
background following the approach developed by the authors in Mason-Nicolas
2009 for the wave equation. The method combines a conformal compactification
with vector field techniques in order to work out the optimal space of initial
data for a given transverse regularity of the rescaled field across null
infinity. The results show that analogous decay and regularity assumptions in
Minkowski and in Schwarzschild produce the same regularity across null
infinity. The results are valid also for the classes of asymptotically simple
spacetimes constructed by Corvino-Schoen / Chrusciel-Delay.
