Volume 17, issue 3 (2013)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Motivic Brown–Peterson invariants of the rationals

Kyle M Ormsby and Paul Arne Østvær

Geometry & Topology 17 (2013) 1671–1706
Abstract

Let BPn, 0 n , denote the family of motivic truncated Brown–Peterson spectra over . We employ a “local-to-global” philosophy in order to compute the bigraded homotopy groups of BPn. Along the way, we produce a computation of the homotopy groups of BPn over 2, prove a motivic Hasse principle for the spectra BPn, and reprove several classical and recent theorems about the K–theory of particular fields in a streamlined fashion. We also compute the bigraded homotopy groups of the 2–complete algebraic cobordism spectrum MGL over .

Keywords
motivic Adams spectral sequence, algebraic cobordism, algebraic $K$–theory, Hasse principle
Mathematical Subject Classification 2010
Primary: 55T15
Secondary: 19D50, 19E15
References
Publication
Received: 27 August 2012
Revised: 25 February 2013
Accepted: 8 March 2013
Published: 21 June 2013
Proposed: Haynes Miller
Seconded: Paul Goerss, Ralph Cohen
Authors
Kyle M Ormsby
Department of Mathematics
MIT
Cambridge, MA 02139
USA
Paul Arne Østvær
Department of Mathematics
University of Oslo
0316 Oslo
Norway
Department of Mathematics
MIT
Cambridge, MA 02139
USA