发表机构
Simons Laufer Mathematical Sciences Institute (SLMath)（西蒙斯劳弗数学科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在动机同伦理论中证明整数在导出概型S上可逆作用的等价条件，推导得出特定概型上动机球谱的A¹-不变性结论。
AI 中文摘要
我们证明：整数在导出概型S上可逆作用，当且仅当它们在MS_S中仿射直线的约化动机悬浮谱上可逆作用。由此可得，在正则局部诺特概型及存在非零整数作用为零的导出概型上，动机球谱在反转基概型中不可逆的素数后是A¹-不变的；特别地，在正则局部诺特Q-概型上，动机球谱是A¹-不变的。
英文摘要
We show that integers act invertibly on a derived scheme $S$ if and only if they act invertibly on the reduced motivic suspension spectrum of the affine line in $\mathrm{MS}_S$. As a consequence, over regular locally noetherian schemes and derived schemes on which some nonzero integer acts as zero, the motivic sphere spectrum is $\mathbf{A}^1$-invariant after inverting primes that are not invertible in the base scheme. In particular, over regular locally noetherian $\mathbf{Q}$-schemes, the motivic sphere spectrum is $\mathbf{A}^1$-invariant.
Comments3 pages, comments welcome
