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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.
##### MSC:
 14F42 Motivic cohomology; motivic homotopy theory 14L15 Group schemes
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