l-adic algebraic monodromy groups, cocharacters, and the Mumford-Tate conjecture

We prove that the l-adic algebraic monodromy groups associated to a motive over a number field are generated by certain one-parameter subgroups determined by Hedge numbers. In the special case of an abelian variety we obtain stronger statements saying roughly that the l-adic algebraic monodromy groups look like a Mumford-Tate group of some (other?) abelian variety. When the endomorphism ring is Z and the dimension satisfies certain numerical conditions, we deduce the Mumford-Tate conjecture for this abelian variety. We also discuss the problem of finding places of ordinary reduction.