Brown-Peterson spectra in stable A^1-homotopy theory

Abstract

We characterize ring spectra morphisms from the algebraic cobordism spectrum $\QTR{Bbb}{MGL}$ (\QCITE{cite}{}{Vo1}) to an oriented spectrum $\QTR{Bbb}{E}$ (in the sense of Morel \QCITE{cite}{}{Mo}) via formal group laws on the ''topological'' subring $E^{*}=\oplus_iE^{2i,i}$ of $E^{**}$. This result is then used to construct for any prime $p$ a motivic Quillen idempotent on $\QTR{Bbb}{MGL}_{(p)}$. This defines the $BP$-spectrum associated to the prime $p$ as in Quillen's \QCITE{cite}{}{Q1} for the complex-oriented topological case.