  This is a companion paper to our previous work, where we proved the
finiteness of the Tate-Shafarevich group for an arbitrary torus $T$ over a
finitely generated field $K$ with respect to any divisorial set $V$ of places
of $K$. Here, we extend this result to any $K$-group $D$ whose connected
component is a torus (for the same $V$), and as a consequence obtain a
finiteness result for the local-to-global conjugacy of maximal tori in
reductive groups over finitely generated fields. Moreover, we prove the
finiteness of the Tate-Shafarevich group for tori over function fields $K$ of
normal varieties defined over base fields of characteristic zero and satisfying
Serre's condition (F), in which case $V$ consists of the discrete valuations
associated with the prime divisors on the variety (geometric places). In this
situation, we also establish the finiteness of the number of $K$-isomorphism
classes of algebraic $K$-tori of a given dimension having good reduction at all
$v \in V$, and then discuss ways of extending this result to positive
characteristic. Finally, we prove the finiteness of the number of isomorphism
classes of forms of an absolutely almost simple group defined over the function
field of a complex surface that have good reduction at all geometric places.

Algebraic Geometry;Group Theory;Number Theory