## Homotopy Invariance of Nisnevich Sheaves with Milnor-Witt Transfers

##### Doc. Math. 24, 2339-2379 (2019)
DOI: 10.25537/dm.2019v24.2339-2379

### Summary

The category of finite Milnor-Witt correspondences, introduced by Calmès and Fasel, provides a new type of correspondences closer to the motivic homotopy theoretic framework than Suslin-Voevodsky's finite correspondences. A fundamental result in the theory of ordinary correspondences concerns homotopy invariance of sheaves with transfers, and in the present paper we address this question in the setting of Milnor-Witt correspondences. Employing techniques due to Druzhinin, Fasel-Østvær and Garkusha-Panin, we show that homotopy invariance of presheaves with Milnor-Witt transfers is preserved under Nisnevich sheafification.

### Mathematics Subject Classification

14F05, 14F20, 14F35, 14F42, 19E15

### Keywords/Phrases

motives, Milnor-Witt K-theory, Chow-Witt groups, motivic homotopy theory

### References

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### Affiliation

Kolderup, Håkon
University of Oslo, Postboks 1053, Blindern, 0316 Oslo, Norway