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2019 On equivariant and motivic slices
Drew Heard
Algebr. Geom. Topol. 19(7): 3641-3681 (2019). 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 , 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 , B P n 2 for 1 n .

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Drew Heard. "On equivariant and motivic slices." Algebr. Geom. Topol. 19 (7) 3641 - 3681, 2019. https://doi.org/10.2140/agt.2019.19.3641

Information

Received: 1 August 2018; Revised: 15 March 2019; Accepted: 8 April 2019; Published: 2019
First available in Project Euclid: 3 January 2020

zbMATH: 07162216
MathSciNet: MR4045363
Digital Object Identifier: 10.2140/agt.2019.19.3641

Subjects:
Primary: 14F42, 55P91
Secondary: 18E30, 55N20, 55P42

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 7 • 2019
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