  The exact momentum conservation laws for the nonlinear gyrokinetic
Vlasov-Poisson equations are derived by applying the Noether method on the
gyrokinetic variational principle [A. J. Brizard, Phys. Plasmas {\bf 7}, 4816
(2000)]. From the gyrokinetic Noether canonical-momentum equation derived by
the Noether method, the gyrokinetic parallel momentum equation and other
gyrokinetic Vlasov-moment equations are obtained. In addition, an exact
gyrokinetic toroidal angular-momentum conservation law is derived in
axisymmetric tokamak geometry, where the transport of parallel-toroidal
momentum is related to the radial gyrocenter polarization, which includes
contributions from the guiding-center and gyrocenter transformations.
