Bost-Connes systems and F1-structures in Grothendieck rings, spectra, and Nori 
motives

Lieber, Joshua F.; Manin, Yuri I.; Marcolli, Matilde

doi:10.1017/9781108877855.006

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Bost-Connes systems and F₁-structures in Grothendieck rings, spectra, and Nori motives

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Manin, Yuri I.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1017/9781108877855.006
(Publisher version)

https://doi.org/10.48550/arXiv.1901.00020
(Preprint)

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Citation

Lieber, J. F., Manin, Y. I., & Marcolli, M. (2022). Bost-Connes systems and F₁-structures in Grothendieck rings, spectra, and Nori motives. In P. Aluffi, D. Anderson, M. Hering, M. Mustaţă, & S. Payne (Eds.), Facets of algebraic geometry: a collection in honor of William Fulton's 80th birthday (pp. 147-227). Cambridge: Cambridge University Press.

Cite as: https://hdl.handle.net/21.11116/0000-000A-9F06-D

Abstract

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 motives. These categorifications are related to the integral
Bost-Connes algebra via suitable Euler characteristic type maps and zeta
functions, and in the motivic case via fiber functors. We also discuss aspects
of F1-geometry, in the framework of torifications, that fit into this general
setting.