论文标题
连接$ k（1）$的动机类似物的切片频谱序列 - 本地球
The slice spectral sequence for a motivic analogue of the connective $K(1)$-local sphere
论文作者
论文摘要
我们计算了$ l $的动机稳定同型组的切片频谱序列，这是一个共同的$ k（1）$的动机类似物 - 特征性特征的主要领域，而不是两个。加上代数闭合场上的类似计算，这会产生有关动机$ k（1）$ - 本地球的信息，而不是两个特征的基本领域。为了计算切片频谱序列，我们证明了可能具有独立感兴趣的几个结果。我们用动机频谱序列描述了$ d_1 $ -Differentials，这是基于Ananyevskiy，r {Ö} ndigs和Østvær的类似结果，以基于Hermitian K Theyory的非常有效的封面。我们还明确描述了某些动机Eilenberg--Maclane光谱的系数，并计算片段频谱序列，以使Hermitian K理论在Prime领域的非常有效的覆盖率。
We compute the slice spectral sequence for the motivic stable homotopy groups of $L$, a motivic analogue of the connective $K(1)$-local sphere over prime fields of characteristic not two. Together with the analogous computation over algebraically closed fields, this yields information about the motivic $K(1)$-local sphere over arbitrary base fields of characteristic not two. To compute the slice spectral sequence, we prove several results which may be of independent interest. We describe the $d_1$-differentials in the slice spectral sequence in terms of the motivic Steenrod operations over general base fields, building on analogous results of Ananyevskiy, R{ö}ndigs, and Østvær for the very effective cover of Hermitian K-theory. We also explicitly describe the coefficients of certain motivic Eilenberg--MacLane spectra and compute the slice spectral sequence for the very effective cover of Hermitian K-theory over prime fields.
