Motivic invariants of p-adic fields

Abstract

We 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> over p-adic fields. These spectra interpolate between integral motivic cohomology (n=0), a connective version of algebraic K-theory (n=1), and the algebraic Brown-Peterson spectrum. We deduce that, over p-adic fields, the 2-complete BPGL<n> split over 2-complete BPGL<0>, implying that the slice spectral sequence for BPGL collapses. This is the first in a series of two papers investigating motivic invariants of p-adic fields, and it lays the groundwork for an understanding of the motivic Adams-Novikov spectral sequence over such base fields.

19 pages, 3 figures. Substantially updated from initial version to better reflect the version of the paper published a year ago

Cited by in corpus (5)

• Motivic Brown-Peterson invariants of the rationals
• Two-complete stable motivic stems over finite fields
• Examples of non-algebraic classes in the Brown-Peterson tower
• A Thom Spectrum Model for $C_2$-Integral Brown--Gitler Spectra
• The motivic lambda algebra and motivic Hopf invariant one problem