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math.AG2021
From Six Functors Formalisms to Derived Motivic Measures
Joshua Lieber
In this paper, we generally describe a method of taking an abstract six functors formalism in the sense of Khan or Cisinski-Déglise, and outputting a derived motivic measure in the…
math.AG2019
Bost-Connes systems and F1-structures in Grothendieck rings, spectra, and Nori motives
Joshua F. Lieber, Yuri I. Manin, Matilde Marcolli
We construct geometric lifts of the Bost-Connes algebra to Grothendieck rings and to the associated assembler categories and spectra, as well as to certain categories of Nori motiv…