  In this paper, we show some applications to algebraic cycles by using higher
Abel-Jacobi maps which were defined in [the author: Motives and algebraic de
Rham cohomology]. In particular, we prove that the Beilinson conjecture on
algebraic cycles over number fields implies the Bloch conjecture on zero-cycles
on surfaces. Moreover, we construct a zero-cycle on a product of curves whose
Mumford invariant vanishes, but not higher Abel-Jacobi invariant.
