Ext群H0v2{-1}BP*[t1]/(4,v1∞))
he $Ext$ groups $H^0v_2^{-1}BP_*[t_1]/(4,v_1^infty))$
令$T(1)$为Ravenel谱,$T(1)/(4)$为$4:T(1)longrightarrow T(1)$的上纤维,$L_2$为对于$v_2^{-1}BP$的局部化函子。为利用Adams-Novikov谱序列计算$L_2T(1)/(4)$的同伦群,首先需要计算出$Ext$群$Ext_{BP_*BP}^{s,t}(BP_*, v_2^{-1}BP_*[t_1]/(4,v_1^infty)$。本文从$H^*M_1^1[t_1]$出发利用$2$-Bockstein谱序列计算出了$Ext$ 群$Ext_{BP_*BP}^0(BP_*, v_2^{-1}BP_*[t_1]/(4, v_1^infty))=H^0v_2^{-1}BP_*[t_1]/(4,v_1^infty)$
Let $T(1)$ be the Ravenel spectrum, $T(1)/(4)$ be the cofiber of$4: T(1)longrightarrow T(1)$ and $L_2$ be the localization functor with respect to $v_2^{-1}BP$.To determine the homotopy groups of $L_2T(1)/(4)$, one need to start with determine the $Ext$ groups$Ext_{BP_*BP}^{s,t}(BP_*, v_2^{-1}BP_*[t_1]/(4,v_1^infty)$. In this paper, we determinethe $Ext$ groups $Ext_{BP_*BP}^0(BP_*, v_2^{-1}BP_*[t_1]/(4, v_1^infty))=H^0v_2^{-1}BP_*[t_1]/(4,v_1^infty)$by the $2$-Bockstein spectral sequence with$E_1$-term $H^*M_1^1[t_1]$.
赵东旭、王向军
数学
拓扑学稳定同伦Adams-Novikov谱序列Bockstein谱序列
opology stable homotopy Adams-Novikov spectral sequence Bockstein spectral sequence
赵东旭,王向军.Ext群H0v2{-1}BP*[t1]/(4,v1∞))[EB/OL].(2016-06-12)[2025-08-18].http://www.paper.edu.cn/releasepaper/content/201606-580.点此复制
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