  If k is an arbitrary field, we construct a category of k-1-motives in which
every commutative algebraic k-group G has a dual object $G^{\vee}$. When k is a
local field of arbitrary characteristic, we establish Pontryagin duality
theorems that relate the fppf cohomology groups of G to the hypercohomology
groups of the k-1-motive $G^{\vee}$. We also obtain a duality theorem for the
second cohomology group of an arbitrary k-1-motive. These results have
applications (to be discussed elsewhere) to certain extensions of
Lichtenbaum-van Hamel duality to a class of non-smooth proper k-varieties.
