Purity of reciprocity sheaves
Shuji Saito
The purpose of this paper is to prove a conjecture of Kahn-Saito-Yamazaki . This is accomplished by extending Voevodsky's fundamental results on homotopy invariant (pre)sheaves with transfers to its generalizations, reciprocity sheaves and cube-invariant sheaves in the context of theory of modulus (pre)sheave with transfers. The main results of this paper is expected to play a crucial role in deducing the main properties of the triangulated category of motives with modulus, which is a new triangulated category enlarging Voevodsky's triangulated category of motives to encompass non homotopy invariant motivic phenomena.
Reference : Advances in Mathematics https://doi.org/10.1016/j.aim.2020.107067
ArXiv link : https://arxiv.org/abs/1704.02442