Noether’s second theorem for BRST symmetries

We present Noether’s second theorem for graded Lagrangian systems of even and odd variables on an arbitrary body manifold X in a general case of BRST symmetries depending on derivatives of dynamic variables and ghosts of any finite order. As a preliminary step, Noether’s second theorem for Lagrangian systems on fiber bundles Y→X possessing gauge symmetries depending on derivatives of dynamic variables and parameters of arbitrary order is proved.