Purity of reciprocity sheaves

Shuji Saito

Published 2017-04-08Version 1

The purpose of this paper is to extend Voevodsky's fundamental results on homotopy invariant (pre)sheaves with transfers to its generalization, reciprocity (pre)sheaves introduced by Kahn-Saito-Yamazaki. The main results of this paper play a crucial role in deducing the main properties of the triangulated category of motives with modulus constructed by Kahn-Saito-Yamazaki, which is a new triangulated category enlarging Voevodsky's triangulated category of motives to encompass non homotopy invariant motivic phenomena.