Structure of the energy-momentum tensor and the spin tensor in a covariant theory of a spinor field

A covariant generalization of the second part of Noether's theorem is obtained for a spinor field in Riemannian space-time. Differential relations for the energy-momentum tensor and the spin tensor are derived from the conditions of invariance of the field equations with respect to arbitrary infinitesimal variations of the coordinates and the tetrad components. The symmetrization of the energy-momentum tensor of the spinor field is considered.