Last updated 16 Aug 2018.
Definition 2.4: only the second characterization of G^{1,Zar}_l,
as the kernel of the map G^{Zar}_l -> G_m, is correct. The first
characterization does give the right connected part by Bogomolov's theorem,
but the component group may be too small (depending on l).
Definition 2.9: Taking the semisimple component is unnecessary, as a theorem
of Tate implies that g'_p is itself semisimple (since we only consider
motives associated to abelian varieties).
Definition 2.11: the reference to [Del82, Proposition 6.2] should be to [Del82, Corollary 6.2].
Definition 2.20: the first instance of Gal(L/k) should be G_k.
Definition 3.1: the statement of (ST2) is incomplete; it should also include
the condition that the Hodge circles must generate a
dense subgroup of G. This is needed to rule out the group U(2) embedded
as the centralizer of U(1) as in section 3.4.
End of section 4.6: the index 2 subgroups of J(C_2) are C_2, J(C_1), and
C_{2,1}, not J(C_1), J(C_1), C_2 as written.
(We thank Jeroen Sijsling for bringing this to our attention.)
Table 6: The component (ac)^2G_1 is listed in the wrong row, it should
appear in the row below beside abG_1, with a1=0 and a2=2.
(We thank Edgar Costa for bringing this to our attention.)