Motivic Brown-Peterson invariants of the rationals

Abstract

Fix the base field Q of rational numbers and let BP<n> denote the family of motivic truncated Brown-Peterson spectra over Q. We employ a "local-to-global" philosophy in order to compute the motivic Adams spectral sequence converging to the bi-graded homotopy groups of BP<n>. Along the way, we provide a new computation of the homotopy groups of BP<n> over the 2-adic rationals, prove a motivic Hasse principle for the spectra BP<n>, and deduce several classical and recent theorems about the K-theory of particular fields.

32 pages, 6 figures; Introduction and exposition improved, typos corrected, now published in Geometry & Topology

References in corpus (3)

• From algebraic cobordism to motivic cohomology
• Chern classes, K-theory and Landweber exactness over nonregular base schemes
• Ext and the Motivic Steenrod Algebra over $\mathbb{R}$

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• Motivic Hopf elements and relations
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• On equivariant and motivic slices
• Algebraic cobordism of number fields
• Stable motivic pi_1 of low-dimensional fields
• The motivic lambda algebra and motivic Hopf invariant one problem