论文标题
动机稳定共同动物和单型排
Motivic stable cohomotopy and unimodular rows
论文作者
论文摘要
我们将范德·卡伦（Van der Kallen）的群体结构与平滑的代数$ a $相对于字段$ k $的值联系起来，并与$ a $ a $ a $ a $ a spectrigients的动机共同体群体相关联，$ \ mathbb {a}^a}^n \ setminus 0 $ septric spectrum spectrum spectrum。在上一节中，我们比较了本文中研究的动机共同动物理论，并由$ \ mathbb {a}^{n+1} \ setMinus 0 $ 0 $或等效地，由$ \ mathbb {a} a}^1 $ - weake^1 $ - weakly等等的Quadric Quadric quad $ q_ {2n+1} $ wistirated as qu _ {2n+1} $，以及该QUAD和FAS。 $ q_ {2n} $，通过显式形态$ q_ {2n+1} \ rightarrow q_ {2n} $，$ q_ {2n} \ times \ times \ mathbb {g} _m \ rightArrow q__m \ rightarrow q_ {2n+1} $ quadrics的$。
We relate the group structure of van der Kallen on orbit sets of unimodular rows with values in a smooth algebra $A$ over a field $k$ with the motivic cohomotopy groups of the spectrum of $A$ with coefficients in $\mathbb{A}^n\setminus 0$ in the sense of Asok and Fasel. In the last section, we compare the motivic cohomotopy theory studied in this paper and defined by $\mathbb{A}^{n+1}\setminus 0$ or, equivalently, by an $\mathbb{A}^1$-weakly equivalent quadric $Q_{2n+1}$ to that considered by Asok and Fasel, defined by a quadric $Q_{2n}$, by means of explicit morphisms $Q_{2n+1}\rightarrow Q_{2n}$, $Q_{2n}\times\mathbb{G}_m\rightarrow Q_{2n+1}$ of quadrics.
