Mayer-Vietoris triangles for motives with modulus

TL;DR

This paper constructs Mayer-Vietoris triangles in the category of motives with modulus, enabling a new description of the effective geometric motives category, thereby refining previous results in the field.

Contribution

It introduces MV squares in the category of modulus pairs, providing a new framework to describe the category of effective geometric motives with modulus.

Findings

Construction of MV squares in the category of modulus pairs.

New description of the category of effective geometric motives with modulus.

Refinement of previous results on motives with modulus.

Abstract

We construct "MV squares" in the category $\mathbf{MCor}$ of modulus pairs which was introduced in arXiv:1511.07124 [math:AG]. They allow us to describe the category $\mathbf{MDM}_{\mathrm{gm}}^{\mathrm{eff}}$ of loc. cit. in a similar way as Voevodskys category $\mathbf{DM}_{\mathrm{gm}}^{\mathrm{eff}}$, thus sharpening the results of the quoted paper.