English

Motivic invariants of p-adic fields

Algebraic Topology 2012-11-02 v2 Algebraic Geometry K-Theory and Homology

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.

Keywords

Cite

@article{arxiv.1002.5007,
  title  = {Motivic invariants of p-adic fields},
  author = {Kyle M. Ormsby},
  journal= {arXiv preprint arXiv:1002.5007},
  year   = {2012}
}

Comments

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