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Motivic invariants of p-adic fields

Published online by Cambridge University Press:  19 May 2011

Kyle M. Ormsby
Kyle M. Ormsby
Affiliation:
Massachusetts Institute of Technology, Department of Mathematics, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USAormsby@math.mit.edu
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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〈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 (n = ∞). We deduce that, over p-adic fields, the 2-complete BPGL〈n〉 splits 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

motivic Adams spectral sequencealgebraic K-theoryalgebraic cobordism

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Type
Research Article
Information
Journal of K-Theory , Volume 7 , Issue 3 , June 2011 , pp. 597 - 618
Copyright
Copyright © ISOPP 2011

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