Abstract
We relate the group structure of van der Kallen on orbit sets of unimodular rows ([26]) with values in a smooth algebra A over a field k with the motivic cohomotopy groups of X=SpecA with coefficients in An∖0 in the sense of [5]. In the last section, we compare the motivic cohomotopy theory studied in this paper and defined by An+1∖0 or, equivalently, by an A1-weakly equivalent quadric Q2n+1 to that considered in [5], defined by a quadric Q2n, by means of explicit morphisms Q2n+1→Q2n, Q2n×Gm→Q2n+1 of quadrics.
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