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In this note, without the assumption of resolution of singularities, we provean equivalence between the category of motives with modulus in positivecharacteristic with rational coefficient $\MDM^\eff(k,\Q)$ and Voevodsky'scategory of motives $\DM^\eff(k,\Q)$, which has been philosophically predictedfrom the beginning in the study of motives with modulus.

A comparison theorem between Voevodsky's motives and motives with modulus in positive characteristic with rational coefficient