Let BP, 0 ≤ n ≤ ∞, denote the family of motivic truncated Brown-Peterson spectra over Q. We employ a "local-to-global" philosophy in order to compute the bigraded homotopy groups of BP. Along the way, we produce a computation of the homotopy groups of BP over Q_2, prove a motivic Hasse principle for the spectra BP, 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 Q.
展开▼
