2022/04/19 by Zhipeng Duan, Duan, Zhipeng, Guchuan Li +3 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2204.08600
openalex publication_date 2022/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that at the prime 2, for any height h and any finite subgroup G ⊂ \mathbbGh of the Morava stabilizer group, the RO(G)-graded homotopy fixed point spectral sequence for the Lubin--Tate spectrum Eh has a strong horizontal vanishing line of filtration Nh, G, a specific number depending on h and G. It is a consequence of the nilpotence theorem that such homotopy fixed point spectral sequences all admit strong horizontal vanishing lines at some finite filtration. Here, we establish specific bounds for them. Our bounds are sharp for all the known computations of EhhG. Our approach involves investigating the effect of the Hill--Hopkins--Ravenel norm functor on the slice differentials. As a result, we also show that the RO(G)-graded slice spectral sequence for (NC2Gvh)-1BP( (G) ) shares the same horizontal vanishing line at filtration Nh, G. As an application, we utilize this vanishing line to establish a bound on the orientation order Θ(h, G), the smallest number such that the Θ(h, G)-fold direct sum of any real vector bundle is EhhG-orientable.