Duke Mathematical Journal
- Duke Math. J.
- Volume 167, Number 8 (2018), 1525-1571.
On the conservativity of the functor assigning to a motivic spectrum its motive
Given a -connective motivic spectrum over a perfect field , we determine of the associated motive in terms of . Using this, we show that if has finite -étale cohomological dimension, then the functor 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 -étale cohomological dimension by considering what we call real motives.
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
Permanent link to this document
Digital Object Identifier
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]
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