Volume 19, issue 7 (2019)

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On equivariant and motivic slices

Drew Heard

Algebraic & Geometric Topology 19 (2019) 3641–3681

Let k be a field with a real embedding. We compare the motivic slice filtration of a motivic spectrum over Spec(k) with the C2 –equivariant slice filtration of its equivariant Betti realization, giving conditions under which realization induces an equivalence between the associated slice towers. In particular, we show that, up to reindexing, the towers agree for all spectra obtained from localized quotients of MGL and M, and for motivic Landweber exact spectra and their realizations. As a consequence, we deduce that equivariant spectra obtained from localized quotients of M are even in the sense of Hill and Meier, and give a computation of the slice spectral sequence converging to π,BPn2 for 1 n .

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motivic homotopy, equivariant homotopy theory, slice filtration, slice spectral sequence
Mathematical Subject Classification 2010
Primary: 14F42, 55P91
Secondary: 18E30, 55N20, 55P42
Received: 1 August 2018
Revised: 15 March 2019
Accepted: 8 April 2019
Published: 17 December 2019
Drew Heard
Fakultät für Mathematik
Universität Regensburg