  In this paper, we formulate and prove a duality for cohomology of curves over
perfect fields of positive characteristic with coefficients in Neron models of
abelian varieties. This is a global function field version of the author's
previous work on local duality and Grothendieck's duality conjecture. It
generalizes the perfectness of the Cassels-Tate pairing in the finite base
field case. The proof uses the local duality mentioned above, Artin-Milne's
global finite flat duality, the non-degeneracy of the height pairing and
finiteness of crystalline cohomology. All these ingredients are organized under
the formalism of the rational etale site developed earlier.
