Skip to main content

Research Repository

Advanced Search

Affine quadrics and the Picard group of the motivic category

Vishik, Alexander



In this paper we study the subgroup of the Picard group of Voevodsky's category of geometric motives DMgm(k; 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.


Vishik, A. (2019). Affine quadrics and the Picard group of the motivic category. Compositio Mathematica, 155(8), 1500-1520.

Journal Article Type Article
Acceptance Date Apr 3, 2019
Online Publication Date Jul 4, 2019
Publication Date Aug 1, 2019
Deposit Date Nov 19, 2018
Publicly Available Date Nov 19, 2018
Journal Compositio Mathematica
Print ISSN 0010-437X
Electronic ISSN 1570-5846
Publisher Foundation Compositio Mathematica
Peer Reviewed Peer Reviewed
Volume 155
Issue 8
Pages 1500-1520
Keywords Algebra and Number Theory
Public URL
Publisher URL


You might also like

Downloadable Citations