Duke Mathematical Journal

On the conservativity of the functor assigning to a motivic spectrum its motive

Tom Bachmann

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Given a 0-connective motivic spectrum ESH(k) over a perfect field k, we determine h̲0 of the associated motive MEDM(k) in terms of π̲0(E). Using this, we show that if k has finite 2-étale cohomological dimension, then the functor M:SH(k)DM(k) is conservative when restricted to the subcategory of compact spectra and induces an injection on Picard groups. We extend the conservativity result to fields of finite virtual 2-étale cohomological dimension by considering what we call real motives.

Article information

Duke Math. J., Volume 167, Number 8 (2018), 1525-1571.

Received: 11 March 2016
Revised: 21 December 2017
First available in Project Euclid: 28 March 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F42: Motivic cohomology; motivic homotopy theory [See also 19E15]
Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]

motivic homotopy theory conservativity slice filtration motives


Bachmann, Tom. On the conservativity of the functor assigning to a motivic spectrum its motive. Duke Math. J. 167 (2018), no. 8, 1525--1571. doi:10.1215/00127094-2018-0002. https://projecteuclid.org/euclid.dmj/1522224100

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