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On stably trivial spin torsors over low-dimensional schemes. (English) Zbl 1420.14046
Summary: The paper discusses stably trivial torsors for spin and orthogonal groups over smooth affine schemes over infinite perfect fields of characteristic unequal to 2. We give a complete description of all the invariants relevant for the classification of such objects over schemes of dimension at most 3, along with many examples. The results are based on the \(\mathbb{A}^1\)-representability theorem for torsors and transfer of known computations of \(\mathbb{A}^1\)-homotopy sheaves along the sporadic isomorphisms to spin groups.
14F42 Motivic cohomology; motivic homotopy theory
14L15 Group schemes
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