  We present a conjectural formula describing the cokernel of the Albanese map
of zero-cycles of smooth projective varieties $X$ over $p$-adic fields in terms
of the N\'eron-Severi group and provide a proof under additional assumptions on
an integral model of $X$. The proof depends on a non-degeneracy result of
Brauer-Manin pairing due to Saito-Sato and on Gabber-de Jong's comparison
result of cohomological- and Azumaya-Brauer groups. We will also mention the
local-global problem of the Albanese-cokernel; the abelian group on the "local
side" turns out to be a finite group.
