论文标题
用于紧凑的谎言组动作的乘法泰特光谱序列
A multiplicative Tate spectral sequence for compact Lie group actions
论文作者
论文摘要
给定一个紧凑的谎言组$ g $和可交换的正交环频谱$ r $，使得$ r [g] _*=π_*（r \ wedge g _+）$是有限生成的，并且超过$π_**（r）$，我们构建了$ g $ g $ - $ g $ - $ r $ $ r $ r $ x $ x $ x的$ x $ x $ xmod $ xmod $ xmod $ xmodule x orth $ e^2 $ - 由$ r [g] _*$的Hopf代数泰特共同体给出，系数为$π_*（x）$。在轻度假设下，例如$ x $在下面的界限和派生的页面$ re^\ infty $消失，此频谱序列与$ g $ g $ - tate $ x^{tg}^{tg} = [tg^{tg} = [\ deteteDeLe {\ gg $ geg $ g $ g $ x^g $ g $ g $ x^g $的同型$π_**（x^{tg}）$强烈收敛。
Given a compact Lie group $G$ and a commutative orthogonal ring spectrum $R$ such that $R[G]_* = π_*(R \wedge G_+)$ is finitely generated and projective over $π_*(R)$, we construct a multiplicative $G$-Tate spectral sequence for each $R$-module $X$ in orthogonal $G$-spectra, with $E^2$-page given by the Hopf algebra Tate cohomology of $R[G]_*$ with coefficients in $π_*(X)$. Under mild hypotheses, such as $X$ being bounded below and the derived page $RE^\infty$ vanishing, this spectral sequence converges strongly to the homotopy $π_*(X^{tG})$ of the $G$-Tate construction $X^{tG} = [\widetilde{EG} \wedge F(EG_+, X)]^G$.
