Motivic Telescope Conjecture in telescopic form

Let XX be a finite motivic spectrum of type (m,n)(m,n) with a non-nilpotent self-map v:Σr,sXXv:\Sigma^{-r,-s}X\to X of type (m,n)(m,n). Write E\langle E\rangle for the Bousfield class of a motivic spectrum EE, and v1Xv^{-1}X for the telescope of vv. Motivic Telescope Conjecture. The Bousfield class v1X\langle v^{-1}X\rangle depends only on mm and nn, and

v1X=K(βij).\langle v^{-1}X\rangle=\langle K(\beta_{ij})\rangle.

This is the telescopic formulation of the motivic Telescope Conjecture; its relationship with the localization and smashing formulations depends on further conjectural smashing and localization properties.

Sources & referencesView supporting material

Primary source

Dominic Leon Culver and J. D. Quigley, “kq-Resolutions I”, arXiv:1905.11952 (2020).

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