  We prove the Mumford-Tate conjecture for those abelian varieties over number
fields, whose simple factors of their adjoint Mumford-Tate groups have over
$\dbR$ certain (products of) non-compact factors. In particular, we prove this
conjecture for the orthogonal case ($B_n$ and $D_n^{\dbR}$ Shimura types). We
construct embeddings of Shimura varieties of (whose adjoints are of prescribed
abelian type) into unitary Shimura varieties. We also prove two general
theorems involving Frobenius tori of abelian varieties over number fields.
