论文标题
$ ro（g）$ - 分级同拷贝固定点光谱序列$ 2 $ 2 $ MORAVA $ E $ - 理论
$RO(G)$-graded homotopy fixed point spectral sequence for height $2$ Morava $E$-theory
论文作者
论文摘要
我们将$ g = q_8，sd_ {16}，g_ {24}，$和$ g_ {48} $作为Morava稳定器组的有限亚组，该组在高度上作用于$ 2 $ 2 $ 2 $ MORAVA $ E $ - 理论$ \ MATHBF {e} _2 _2 _2 _2 $ PILIDE $ 2 $ 2 $ 2 $。我们完全计算$ \ Mathbf {e} _2 $的$ G $ -HOMOTOPY固定点光谱序列。自Hill，Hopkins和Ravenel以来，我们的计算使用了最近开发的均等技术。我们还计算$（* - σ_i）$ - 分级$ q_8 $ - 和$ sd_ {16} $ - 同型固定点频谱序列，其中$σ_i$是$ q_8 $的非平整一维表示。
We consider $G=Q_8,SD_{16},G_{24},$ and $G_{48}$ as finite subgroups of the Morava stabilizer group which acts on the height $2$ Morava $E$-theory $\mathbf{E}_2$ at the prime $2$. We completely compute the $G$-homotopy fixed point spectral sequences of $\mathbf{E}_2$. Our computation uses recently developed equivariant techniques since Hill, Hopkins, and Ravenel. We also compute the $(*-σ_i)$-graded $Q_8$- and $SD_{16}$-homotopy fixed point spectral sequences, where $σ_i$ is a non-trivial one-dimensional representation of $Q_8$.
