Abstract
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.
Citation
Tom Bachmann. "On the conservativity of the functor assigning to a motivic spectrum its motive." Duke Math. J. 167 (8) 1525 - 1571, 1 June 2018. https://doi.org/10.1215/00127094-2018-0002
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