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arXiv · 2007.08682

Algebraic slice spectral sequences

Dominic Leon Culver·Hana Jia Kong·J. D. Quigley
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Abstract

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 $\mathbb{R}$-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.

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Dominic Leon Culver, Hana Jia Kong, J. D. Quigley. 2021-08-18. Algebraic slice spectral sequences. https://arxiv.org/abs/2007.08682

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