Geodesic
On the Invertibility of Motives of Affine Quadrics
Documenta mathematica, Tome 22 (2017), pp. 363-395.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We show that the reduced motive of a smooth affine quadric is invertible as an object of the triangulated category of motives $\bold{DM}(k,\Bbb Z[1/e])$ (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) $\bold{DM}(k,\Bbb Z[1/e])$, the construction of which constitutes the main part of this work.
Classification : 14C15, 11E04, 14C25
Keywords: quadric, motive, invertible 
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     author = {Bachmann, Tom},
     title = {On the {Invertibility} of {Motives} of {Affine} {Quadrics}},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a41/}
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Bachmann, Tom. On the Invertibility of Motives of Affine Quadrics. Documenta mathematica, Tome 22 (2017), pp. 363-395. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a41/