  We study conserved currents of any integer or half integer spin built from
massless scalar and spinor fields in $AdS_3$. 2-forms dual to the conserved
currents in $AdS_3$ are shown to be exact in the class of infinite expansions
in higher derivatives of the matter fields with the coefficients containing
inverse powers of the cosmological constant. This property has no analog in the
flat space and may be related to the holography of the AdS spaces.
