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arXiv · 1002.5007

Motivic invariants of p-adic fields

Kyle M. Ormsby
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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 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 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.

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Kyle M. Ormsby. 2012-11-01. Motivic invariants of p-adic fields. https://doi.org/10.1017/is011004017jkt153

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