Stable birational localization over arbitrary fields

Determine whether the identification of stable n-birational localization with the Tate truncation functor f_{0/n+1} holds over arbitrary fields, rather than only over perfect fields.

Background

The paper identifies the stable n-birational motivic homotopy category with the Tate-truncated category mathcal{SH}^{S^1}(k)/f_{n+1} over perfect fields. This identification allows the authors to transfer the connectivity theorem for Tate truncations to stable n-birational localization and thereby prove connectivity preservation in the perfect-field case.

The corresponding identification is not established over arbitrary fields, leaving open whether stable n-birational localization is generally modeled by the Tate truncation f_{0/n+1}. Resolving this would extend the stable birational connectivity results beyond perfect fields.