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 $E^{\ast }={\oplus }_i{E}^{2i,i}$ of $E^{\ast \ast }$. 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.

arXiv comment14 pages; a section on motivations has been added

Cited by in corpus (8)

• Triangulated categories of mixed motives
• From algebraic cobordism to motivic cohomology
• On the algebraic cobordism spectra MSL and MSp
• Orientation theory in arithmetic geometry
• On the relation of Voevodsky's algebraic cobordism to Quillen's K-theory
• The Adams-Novikov spectral sequence and Voevodsky's slice tower
• Motivic Brown-Peterson invariants of the rationals
• Triangulated categories of motives in positive characteristic