论文标题
$η$ - 周期动机稳定同义理论
$η$-periodic motivic stable homotopy theory over fields
论文作者
论文摘要
在任何特征的领域而不是2个领域，我们通过结缔组织2-Local witt K理论频谱的偏移来建立$η$ - 周期性2个环境动机球谱的2项分辨率。这与经典稳定同型理论中K（1） - 本地球的分辨率相似。作为应用程序，我们确定$η$ priodized的动机稳定茎以及$η$ priodized代数符号和sl-cobobordism群体。一路走来，我们在代表Hermitian K理论的动机频谱上构建了Adams的操作，并为有限的虚拟2-杂色维度领域的某些动机谱创造了新的完整性结果。在附录中，我们为Hermitian K理论的既定固定点定理提供了新的证明。
Over any field of characteristic not 2, we establish a 2-term resolution of the $η$-periodic, 2-local motivic sphere spectrum by shifts of the connective 2-local Witt K-theory spectrum. This is curiously similar to the resolution of the K(1)-local sphere in classical stable homotopy theory. As applications we determine the $η$-periodized motivic stable stems and the $η$-periodized algebraic symplectic and SL-cobordism groups. Along the way we construct Adams operations on the motivic spectrum representing Hermitian K-theory and establish new completeness results for certain motivic spectra over fields of finite virtual 2-cohomological dimension. In an appendix, we supply a new proof of the homotopy fixed point theorem for the Hermitian K-theory of fields.
