Abstract
AbstractWe provide a complete analysis of the motivic Adams spectral sequences converging to the bigraded coefficients of the 2-complete algebraic Johnson-Wilson spectra BPGL〈n〉 overp-adic fields. These spectra interpolate between integral motivic cohomology (n= 0), a connective version of algebraicK-theory (n= 1), and the algebraic Brown-Peterson spectrum (n= ∞). We deduce that, overp-adic fields, the 2-completeBPGL〈n〉 splits over 2-complete BPGL〈0〉, implying that the slice spectral sequence forBPGLcollapses.This is the first in a series of two papers investigating motivic invariants ofp-adic fields, and it lays the groundwork for an understanding of the motivic Adams-Novikov spectral sequence over such base fields.
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