arXiv subjects

Kyle M. Ormsby

Publications and source records attributed to Kyle M. Ormsby.

3 recordsLinked to original sources

arXiv2014

Stable motivic pi_1 of low-dimensional fields

Let k be a field with cohomological dimension less than 3; we call such fields low-dimensional. Examples include algebraically closed fields, finite fields and function fields thereof, local fields, and number fields with no real embeddings. We determine the 1-column of the motivic Adams-Novikov spectral sequence over k. Combined with rational information we use this to compute the first stable motivic homotopy group of the sphere spectrum over k. Our main result affirms Morel's pi_1-conjecture in the case of low-dimensional fields. We also determine stable motivic pi_1 in integer weights other than -2, -3, and -4.

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arXiv2013

Motivic Brown-Peterson invariants of the rationals

Fix the base field Q of rational numbers and let BP 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 . Along the way, we provide a new computation of the homotopy groups of BP over the 2-adic rationals, prove a motivic Hasse principle for the spectra BP , and deduce several classical and recent theorems about the K-theory of particular fields.

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arXiv2012

Motivic invariants of p-adic fields

We provide a complete analysis of the motivic Adams spectral sequences converging to the bigraded coefficients of the 2-complete algebraic Johnson-Wilson spectra BPGL over p-adic fields. These spectra interpolate between integral motivic cohomology (n=0), a connective version of algebraic K-theory (n=1), and the algebraic Brown-Peterson spectrum. We deduce that, over p-adic fields, the 2-complete BPGL split over 2-complete BPGL<0>, implying that the slice spectral sequence for BPGL collapses. This is the first in a series of two papers investigating motivic invariants of p-adic fields, and it lays the groundwork for an understanding of the motivic Adams-Novikov spectral sequence over such base fields.

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