  In this paper, we construct some maps related to the motivic Galois action on
depth-graded motivic multiple zeta values. And from these maps we give some
short exact sequences about depth-graded motivic multiple zeta values in depth
two and three. In higher depth we conjecture that there are exact sequences of
the same type. And we will show from three conjectures about depth-graded
motivic Lie algebra we can nearly deduce the exact sequences conjectures in
higher depth. At last we give a new proof of the result that the modulo
zeta(2)$ version motivic double zeta values is generated by the totally odd
part. And we reduce the well-known conjecture that the modulo zeta (2) version
motivic triple zeta values is generated by the totally odd part to an
isomorphism conjecture in linear algebra.
