Reciprocity sheaves and logarithmic motives

Abstract

We connect two developments aiming at extending Voevodsky's theory of motives over a field in such a way to encompass non-${\mathbf{A}}^1$-invariant phenomina. One is theory of reciprocity sheaves introduced by Kahn-Saito-Yamazaki. Another is theory of the triangulated category ${\mathrm{logDM}}^{\mathrm{eff}}$ of logarithmic motives launched by Binda, Park and Østvær. We prove that the Nisnevich cohomology of reciprocity sheaves is representable in ${\mathrm{logDM}}^{\mathrm{eff}}$.