On equivariant and motivic slices

Heard, Drew

doi:10.2140/agt.2019.19.3641

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On equivariant and motivic slices

Drew Heard

Algebraic & Geometric Topology 19 (2019) 3641–3681

DOI: 10.2140/agt.2019.19.3641

Abstract

Let $k$ be a field with a real embedding. We compare the motivic slice filtration of a motivic spectrum over $Spec (k)$ with the $C_{2}$ –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 $M G L$ and $M ℝ$ , and for motivic Landweber exact spectra and their realizations. As a consequence, we deduce that equivariant spectra obtained from localized quotients of $M ℝ$ are even in the sense of Hill and Meier, and give a computation of the slice spectral sequence converging to $π_{*, *} B P 〈 n 〉 ∕ 2$ for $1 \leq n \leq \infty$ .

Keywords

motivic homotopy, equivariant homotopy theory, slice filtration, slice spectral sequence

Mathematical Subject Classification 2010

Primary: 14F42, 55P91

Secondary: 18E30, 55N20, 55P42

References

Publication

Received: 1 August 2018

Revised: 15 March 2019

Accepted: 8 April 2019

Published: 17 December 2019

Authors

Drew Heard
Fakultät für Mathematik Universität Regensburg Regensburg Germany
https://drew-heard.github.io/

Volume 19, issue 7 (2019)