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

Full text: dvi.gz 71 k, dvi 168 k, ps.gz 425 k, pdf 348 k.

Home Page of DOCUMENTA MATHEMATICA