In this article, we study a spectrum such that is the Grothendieck ring of varieties and such that the higher homotopy groups contain more geometric information about the geometry of varieties. We use the topology of this spectrum to analyze the structure of and to show that classes in the kernel of multiplication by can always be represented as , where , , and are not piecewise-isomorphic, but in . Along the way, we present a new proof of the result of Larsen–Lunts on the structure on .
"The annihilator of the Lefschetz motive." Duke Math. J. 166 (11) 1989 - 2022, 15 August 2017. https://doi.org/10.1215/00127094-0000016X