Witt层与$η$倒球谱
Witt sheaves and the $η$-inverted sphere spectrum
摘要：
Ananyevsky最近计算了理性维特理论的稳定运算和合作。这些计算使我们能够展示塞尔有限性结果的动机模拟：定理：令$k$是一个场。则$π^{\mathbb{A}^1}_ n(\mathbb{S}^- _k )_*$是$n > 0$的挠率。作为应用，我们在$k$上定义了一类Witt动机，并证明了这类动机在理性上等价于$SH(k)_\mathbb{Q}$的负部分.
英文摘要：
Ananyevsky has recently computed the stable operations and cooperations of rational Witt theory. These computations enable us to show a motivic analog of Serre's finiteness result: Theorem: Let $k$ be a field. Then $π^{\mathbb{A}^1}_ n(\mathbb{S}^- _k )_*$ is torsion for $n > 0$. As an application we define a category of Witt motives over $k$ and show that rationally this category is equivalent to the minus part of $SH(k)_\mathbb{Q}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
