  For a complex projective manifold, Walker has defined a regular homomorphism
lifting Griffiths' Abel-Jacobi map on algebraically trivial cycle classes to a
complex abelian variety, which admits a finite homomorphism to the Griffiths
intermediate Jacobian. Recently Suzuki gave an alternate, Hodge-theoretic,
construction of this Walker Abel-Jacobi map. We provide a third construction
based on a general lifting property for surjective regular homomorphisms, and
prove that the Walker Abel-Jacobi map descends canonically to any field of
definition of the complex projective manifold. In addition, we determine the
image of the l-adic Bloch map restricted to algebraically trivial cycle classes
in terms of the coniveau filtration.

Algebraic Geometry