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 E_(2)at the prime 2.We completely compute the G-homotopy fixed point spectral ...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 E_(2)at the prime 2.We completely compute the G-homotopy fixed point spectral sequences of 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,whereσ_(i)is a non-trivial one-dimensional representation of Q_(8).展开更多
首先给出了May谱序列E_1^(s,t,u)项的几个结果,然后利用这些结果和关于Ext_P^(s,t)(Z_p,Z_p)的一个估计(P为由mod p Steenrod代数A的所有循环缩减幂P^i(i≥0)生成的子代数)得出了乘积(?)t (?)g0∈Ext_A^(*,*)(Z_p,Z_p)(3≤t<p-2)在Ad...首先给出了May谱序列E_1^(s,t,u)项的几个结果,然后利用这些结果和关于Ext_P^(s,t)(Z_p,Z_p)的一个估计(P为由mod p Steenrod代数A的所有循环缩减幂P^i(i≥0)生成的子代数)得出了乘积(?)t (?)g0∈Ext_A^(*,*)(Z_p,Z_p)(3≤t<p-2)在Adams谱序列的收敛性。其中g0∈Ext_A^(2,pq+2q)(Z_p,Z_p),(?)∈Ext_A^(3,p^2q+2pq)(Z_p,Z_p).展开更多
基金supported by the National Science Foundation under Grant No.DMS-1926686supported by grant NSFC-12226002,the Shanghai Rising-Star Program under Agreement No.20QA1401600Shanghai Pilot Program for Basic Research-Fudan University 21TQ1400100(21TQ002).
文摘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 E_(2)at the prime 2.We completely compute the G-homotopy fixed point spectral sequences of 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,whereσ_(i)is a non-trivial one-dimensional representation of Q_(8).
文摘首先给出了May谱序列E_1^(s,t,u)项的几个结果,然后利用这些结果和关于Ext_P^(s,t)(Z_p,Z_p)的一个估计(P为由mod p Steenrod代数A的所有循环缩减幂P^i(i≥0)生成的子代数)得出了乘积(?)t (?)g0∈Ext_A^(*,*)(Z_p,Z_p)(3≤t<p-2)在Adams谱序列的收敛性。其中g0∈Ext_A^(2,pq+2q)(Z_p,Z_p),(?)∈Ext_A^(3,p^2q+2pq)(Z_p,Z_p).
基金Supported by NSFC(11301386)NSFC(11001195)+1 种基金Beiyang Elite Scholar Program of Tianjin University(0903061016)The Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
基金Supported by the National Natural Science Foundation of China ( No .10501045) ,the Fund of the personnel Division of Nankai University , the Youth Project ofTianyuan Foundation of China( No .10426028) and the China Postdoctoral ScienceFoundation
