Abstract
The theory of reciprocity sheaves due to Kahn-Saito-Yamazaki is a powerful framework to study invariants of smooth varieties via invariants of pairs (X,D) of a variety X and a divisor D. We develop a generalization of this theory where D can be a Q-divisor. As an application, we provide a motivic construction of the de Rham-Witt complex, which is analogous to the motivic construction of the Milnor K-theory due to Suslin-Voevodsky.
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