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Affine quadrics and the Picard group of the motivic category
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- Journal:
- Compositio Mathematica / Volume 155 / Issue 8 / August 2019
- Published online by Cambridge University Press:
- 04 July 2019, pp. 1500-1520
- Print publication:
- August 2019
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In this paper we study the subgroup of the Picard group of Voevodsky’s category of geometric motives
$\operatorname{DM}_{\text{gm}}(k;\mathbb{Z}/2)$ generated by the reduced motives of affine quadrics. Our main tools here are the functors of Bachmann [On the invertibility of motives of affine quadrics, Doc. Math. 22 (2017), 363–395], but we also provide an alternative method. We show that the group in question can be described in terms of indecomposable direct summands in the motives of projective quadrics over 
$k$. In particular, we describe all the relations among the reduced motives of affine quadrics. We also extend the criterion of motivic equivalence of projective quadrics.
Some Adjunction-Theoretic Properties of Codimension Two Non-Singular Subvarities of Quadrics
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- Journal:
- Canadian Journal of Mathematics / Volume 49 / Issue 4 / 01 August 1997
- Published online by Cambridge University Press:
- 20 November 2018, pp. 675-695
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- 01 August 1997
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