DOCUMENTA MATHEMATICA, Vol. 22 (2017), 363-395

Tom Bachmann

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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