Algebraic tori as Nisnevich sheaves with transfers (Q476080)

Let \(k\) be a field and \(T\) a \(k\)-torus. The author obtains several results that relate the \(R\)-equivalence on tori with homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes. (cf. [\textit{V. Voevodsky} et al., Cycles, transfers, and motivic homology theories. Princeton, NJ: Princeton University Press (2000; Zbl 1021.14006)]) The \(R\)-equivalence classes on tori have been studied by several authors (cf. [\textit{J.-L. Colliot-Thelene} and \textit{J.-J. Sansuc}, Ann. Sci. Éc. Norm. Supér. (4) 10, 175--229 (1977; Zbl 0356.14007); J. Algebra 106, 148--205 (1987; Zbl 0597.14014)]). They are important in many rationality questions. Connecting them to Voevodsky's theory is an interesting feature of this paper and sheds new light on the \(R\)-equivalence.