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.
Cite this article
Håkon Kolderup, Homotopy Invariance of Nisnevich Sheaves with Milnor-Witt Transfers. Doc. Math. 24 (2019), pp. 2339–2379DOI 10.4171/DM/727