This paper focuses on the connection between the Brauer group and
the $0$-cycles of an algebraic variety. We give an alternative
construction of the second $l$-adic Abel-Jacobi map for such cycles,
linked to the algebraic geometry of Severi-Brauer varieties on
$X$. This allows us then to relate this Abel-Jacobi map to the
standard pairing between $0$-cycles and Brauer groups (see [M], [L]),
completing results from [M] in this direction. Second, for surfaces,
it allows us to present this map according to the more geometrical
approach devised by M. Green in the framework of (arithmetic) mixed
Hodge structures (see [G]).
¶ Needless to say, this paper owes much to the work of U. Jannsen
and, especially, to his recently published older letter [J4] to
B. Gross.