Homotopy invariance of Nisnevich sheaves with Milnor-Witt transfers

Abstract

The category of finite Milnor-Witt correspondences, introduced by Calm\`es and Fasel, provides a new type of correspondences closer to the motivic homotopy theoretic framework than Suslin-Voevodsky's correspondences. A fundamental result of 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-{\O}stv{\ae}r and Garkusha-Panin, we show that homotopy invariance of presheaves with Milnor-Witt transfers is preserved under Nisnevich sheafification.