论文标题
通过二元分辨率在$ n = p = 2 $的双重分辨率的摩拉瓦稳定器组
Cohomology of the Morava stabilizer group through the duality resolution at $n=p=2$
论文作者
论文摘要
我们计算Morava稳定器组的连续共同体，具有系数Morava $ e $ - 理论，$ h^*（\ Mathbb {g} _2，e_t）$，$ p = 2 $，at $ p = 2 $，以$ 0 \ leq t <12 $，使用代数t <12 $。此外，在同一范围内，我们计算了$ k（2）$ - 本地球形频谱的同型固定点频谱序列中的$ d_3 $ differentials。这些共同体学组和差异在$ k（2）$ - 本地稳定同型理论中起着核心作用。
We compute the continuous cohomology of the Morava stabilizer group with coefficients in Morava $E$-theory, $H^*(\mathbb{G}_2, E_t)$, at $p=2$, for $0\leq t < 12$, using the Algebraic Duality Spectral Sequence. Furthermore, in that same range, we compute the $d_3$-differentials in the homotopy fixed point spectral sequence for the $K(2)$-local sphere spectrum. These cohomology groups and differentials play a central role in $K(2)$-local stable homotopy theory.
