Geodesic
On the Invertibility of Motives of Affine Quadrics
Documenta mathematica, Tome 22 (2017), pp. 363-395
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We show that the reduced motive of a smooth affine quadric is invertible as an object of the triangulated category of motives DM(k,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) DM(k,Z[1/e]), the construction of which constitutes the main part of this work.
DOI : 10.4171/dm/568
Classification : 11E04, 14C15, 14C25
Mots-clés : motive, quadric, invertible 
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     author = {Tom Bachmann},
     title = {On the {Invertibility} of {Motives} of {Affine} {Quadrics}},
     journal = {Documenta mathematica},
     pages = {363--395},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/568},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/568/}
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Tom Bachmann. On the Invertibility of Motives of Affine Quadrics. Documenta mathematica, Tome 22 (2017), pp. 363-395. doi: 10.4171/dm/568

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