  In our previous study of duality for complete discrete valuation fields with
perfect residue field, we treated coefficients in finite flat group schemes. In
this paper, we treat abelian varieties. This in particular implies
Grothendieck's conjecture on the perfectness of his pairing between the Neron
component groups of an abelian variety and its dual. The point is that our
formulation is well-suited with Galois descent. From the known case of
semistable abelian varieties, we deduce the perfectness in full generality. We
also treat coefficients in tori and, more generally, 1-motives.
