  We prove finiteness results for Tate--Shafarevich groups in degree 2
associated with 1--motives, rely them to Leopoldt's conjecture, and present an
example of a semiabelian variety with an infinite Tate--Shafarevich group in
degree 2. We also establish an arithmetic duality theorem for 1--motives over
number fields which complements earlier results of Harari and Szamuely in this
direction.
