Reciprocity sheaves and logarithmic motives. Issue 2 (13th February 2023) - Saito, Shuji
Abstract : We connect two developments that aim to extend Voevodsky's theory of motives over a field in such a way as to encompass non- $A^1$ -invariant phenomena. One is theory of reciprocity sheaves introduced by Kahn, Saito and Yamazaki. The other is theory of the triangulated category $\operatorname {logDM}^{{\operatorname {eff}}}$ of logarithmic motives launched by Binda, Park and Østvær. We prove that the Nisnevich cohomology of reciprocity sheaves is representable in $\operatorname {logDM}^{{\operatorname {eff}}}$ .