On the Invertibility of Motives of Affine Quadrics
We show that the reduced motive of a smooth affine quadric is invertible as an object of the triangulated category of motives $\DM(k, \ZZ[1/e])$ (where $k$ is a perfect field of exponential characteristic $e$). We also establish a motivic version of the conjectures of Po Hu on products of certain affine Pfister quadrics. Both of these results are obtained by studying a novel conservative functor on (a subcategory of) $\DM(k, \ZZ[1/e])$, the construction of which constitutes the main part of this work.
2010 Mathematics Subject Classification: Primary 14C15; Secondary 11E04, 14C25
Keywords and Phrases: Quadric, motive, invertible
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