  We announce the classification of Sato-Tate groups of abelian threefolds over
number fields; there are 410 possible conjugacy classes of closed subgroups of
USp(6) that occur. We summarize the key points of the "upper bound" aspect of
the classification, and give a more rigorous treatment of the "lower bound" by
realizing 33 groups that appear in the classification as maximal cases with
respect to inclusions of finite index. Further details will be provided in a
subsequent paper.
