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
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).
