For Q-schemes and Dedekind schemes, the motivic t-structure exists on 1-motives with integral coefficients, with heart the abelian category of Deligne 1-motives with torsion.
Th \'e orie des topos et cohomologie \'e tal des sch \'e mas.(sga4) springer lnm 269 and 270, 1972
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Deligne 1-motives with torsion and \'etale motives
For Q-schemes and Dedekind schemes, the motivic t-structure exists on 1-motives with integral coefficients, with heart the abelian category of Deligne 1-motives with torsion.