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.
La r \'e alisation \'e tale et les op \'e rations de Grothendieck , volume 47
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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.