2020/07/16 by Culver, Dominic Leon, Kong, Hana Jia, Quigley, J. D.
#14F42 #55P42 #55P91 #55T05 #55T15 #Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2007.08682
For certain motivic spectra, we construct a square of spectral sequences relating the effective slice spectral sequence and the motivic Adams spectral sequence. We show the square can be constructed for connective algebraic K-theory, motivic Morava K-theory, and truncated motivic Brown-Peterson spectra. In these cases, we show that the ℝ-motivic effective slice spectral sequence is completely determined by the ρ-Bockstein spectral sequence. Using results of Heard, we also obtain applications to the Hill-Hopkins-Ravenel slice spectral sequences for connective Real K-theory, Real Morava K-theory, and truncated Real Brown-Peterson spectra.