Reciprocity sheaves and motives with modulus

Bruno Kahn, Shuji Saito, Takao Yamazaki

Published 2017-07-24Version 1

We exhibit an intimate relationship between "motives with modulus" from arXiv:1511.07124 [math.AG] and "reciprocity sheaves" from arXiv:1402.4201 [math.AG]. Assuming resolution of singularities, we prove that the triangulated category of effective motivic complexes $\mathbf{MDM}^{\mathrm{eff}}$ admits a $t$-structure whose heart is equivalent to the category of reciprocity Nisnevich sheaves. We also give an isomorphism between some Hom groups in $\mathbf{MDM}^{\mathrm{eff}}$ and the hypercohomology of some Suslin complexes with modulus. As an application, we prove some Mayer-Vietoris sequences for Suslin homology with modulus.