紧致李群作用的乘性Tate谱序列
A multiplicative Tate spectral sequence for compact Lie group actions
AI总结：
本文在紧致李群与交换正交环谱的框架下，为正交$G$-谱中的$R$-模构造了乘性$G$-Tate谱序列，并证明在温和假设下强收敛至$G$-Tate构造的同伦群。
摘要：
给定紧致李群$G$与交换正交环谱$R$，若$R[G]_* = π_*(R \wedge G_+)$在$π_*(R)$上有限生成且投射，则对正交$G$-谱中每个$R$-模$X$，构造乘性$G$-Tate谱序列，其$E^2$页为$R[G]_*$以$π_*(X)$为系数的Hopf代数Tate上同调。在温和假设下，如$X$有下界且导出页$RE^\infty$消失，该谱序列强收敛至$G$-Tate构造$X^{tG} = [\widetilde{EG} \wedge F(EG_+, X)]^G$的同伦群$π_*(X^{tG})$。
英文摘要：
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 $X^{tG} = [\widetilde{EG} \wedge F(EG_+, X)]^G$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
