Vol. 2, No. 2, 2017

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Low-dimensional Milnor–Witt stems over $\mathbb R$

Daniel Dugger and Daniel C. Isaksen

Vol. 2 (2017), No. 2, 175–210
Abstract

We compute some motivic stable homotopy groups over . For 0 p q 3, we describe the motivic stable homotopy groups π̂p,q of a completion of the motivic sphere spectrum. These are the first four Milnor–Witt stems. We start with the known Ext groups over and apply the ρ-Bockstein spectral sequence to obtain Ext groups over . This is the input to an Adams spectral sequence, which collapses in our low-dimensional range.

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Keywords
motivic stable homotopy group, motivic Adams spectral sequence, $\rho$-Bockstein spectral sequence, Milnor–Witt stem
Mathematical Subject Classification 2010
Primary: 14F42, 55Q45, 55S10, 55T15
Milestones
Received: 27 May 2015
Revised: 21 March 2016
Accepted: 5 April 2016
Published: 14 December 2016
Authors
Daniel Dugger
Department of Mathematics
University of Oregon
Eugene, OR 97403
United States
Daniel C. Isaksen
Department of Mathematics
Wayne State University
656 W Kirby
Detroit, MI 48202
United States