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

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 (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20200518-093742753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)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1901.00020arXivDiscussion Paper
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.
Funders:
Funding AgencyGrant Number
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
NSFDMS-1707882
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPIN-2018-04937
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPAS-2018-522593
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:18 May 2020 16:43

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