Lieber, Joshua F. and Manin, Yuri I. and Marcolli, Matilde (2018) Bost-Connes systems and F₁-structures in Grothendieck rings, spectra, and Nori motives. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20200518-093742753
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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.
Item Type: | Report or Paper (Discussion Paper) | ||||||||||
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Additional Information: | The first and third authors were supported in part by the Perimeter Institute for Theoretical Physics. The third author is also partially supported by NSF grant DMS-1707882, and by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement grant RGPAS-2018-522593. | ||||||||||
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DOI: | 10.48550/arXiv.1901.00020 | ||||||||||
Record Number: | CaltechAUTHORS:20200518-093742753 | ||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200518-093742753 | ||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||
ID Code: | 103268 | ||||||||||
Collection: | CaltechAUTHORS | ||||||||||
Deposited By: | Tony Diaz | ||||||||||
Deposited On: | 18 May 2020 16:43 | ||||||||||
Last Modified: | 02 Jun 2023 00:44 |
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