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We show that the additive higher Chow groups of regular schemes over a fieldinduce a Zariski sheaf of pro-differential graded algebras, whose Milnor rangeis isomorphic to the Zariski sheaf of big de Rham-Witt complexes. This providesan explicit cycle-theoretic description of the big de Rham-Witt sheaves.Several applications are derived.

de Rham-Witt sheaves via algebraic cycles