  We apply the "trace anomaly method" to the calculation of moments of the
Hawking radiation of a Schwarzschild black hole. We show that they can be
explained as the fluxes of chiral currents forming a W-infinity algebra. Then
we construct the covariant version of these currents and verify that up to
order 6 they are not affected by any trace anomaly. Using cohomological methods
we show that actually, for the fourth order current, no trace anomalies can
exist. The results reported here are strictly valid in two dimensions.
