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arXiv · 1901.00020

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

Joshua F. Lieber·Yuri I. Manin·Matilde Marcolli
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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.

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Joshua F. Lieber, Yuri I. Manin, Matilde Marcolli. 2018-12-31. Bost-Connes systems and F1-structures in Grothendieck rings, spectra, and Nori motives. https://arxiv.org/abs/1901.00020

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