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Matthias Wendt, On stably trivial spin torsors over low-dimensional schemes, The Quarterly Journal of Mathematics, Volume 69, Issue 4, December 2018, Pages 1221–1251, https://doi.org/10.1093/qmath/hay022
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Abstract
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 -representability theorem for torsors and transfer of known computations of -homotopy sheaves along the sporadic isomorphisms to spin groups.
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