Abstract. In this paper we obtain Chevalley's ambiguous class number formula for an arbitrary torus T over a global field. The classical formula of C.Chevalley may be recovered by setting T = Gm in our formula. A key ingredient of the proof is the work of X.Xarles on groups of components of Néron-Raynaud models of tori.

We establish a generalized Cassels-Tate dual exact sequence for 1-motives over global fields. We thereby extend the main theorem of [4] from abelian varieties to arbitrary 1-motives.