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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

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