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On motivic obstructions to Witt cancellation for quadratic forms over schemes

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 نشر من قبل Matthias Wendt
 تاريخ النشر 2018
  مجال البحث
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 تأليف Matthias Wendt




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The paper provides computations of the first non-vanishing $mathbb{A}^1$-homotopy sheaves of the orthogonal Stiefel varieties which are relevant for the unstable isometry classification of quadratic forms over smooth affine schemes over perfect fields of characteristic $ eq 2$. Together with the $mathbb{A}^1$-representability for quadratic forms, this provides the first obstructions for rationally trivial quadratic forms to split off a hyperbolic plane. For even-rank quadratic forms, this first obstruction is a refinement of the Euler class of Edidin and Graham. A couple of consequences are discussed, such as improved splitting results over algebraically closed base fields as well as examples where the obstructions are nontrivial.



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