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

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.

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Item Permalink: https://hdl.handle.net/21.11116/0000-000A-9F06-D Version Permalink: https://hdl.handle.net/21.11116/0000-000E-29A6-9
Genre: Contribution to Festschrift
Latex : Bost-Connes systems and $F_1$-structures in Grothendieck rings, spectra, and Nori motives

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arXiv:1901.00020.pdf (Preprint), 762KB
 
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Lieber-Manin-Marcolli_Bost-Connes systems and F1-structures in Grothendieck rings, spectra, and Nori motives_2022.pdf (Publisher version), 545KB
 
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https://doi.org/10.48550/arXiv.1901.00020 (Preprint)
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 Creators:
Lieber, Joshua F., Author
Manin, Yuri I.1, Author           
Marcolli, Matilde, Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Geometry, Mathematical Physics
 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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Language(s): eng - English
 Dates: 2022
 Publication Status: Issued
 Pages: 81
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: arXiv: 1901.00020
DOI: 10.1017/9781108877855.006
 Degree: -

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Source 1

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Title: Facets of algebraic geometry : a collection in honor of William Fulton's 80th birthday
Source Genre: Festschrift
 Creator(s):
Aluffi, Paolo, Editor
Anderson, David, Editor
Hering, Milena, Editor
Mustaţă, Mircea, Editor
Payne, Sam, Editor
Affiliations:
-
Publ. Info: Cambridge : Cambridge University Press
Pages: - Volume / Issue: 2 Sequence Number: - Start / End Page: 147 - 227 Identifier: ISBN: 978-1-108-79251-6
DOI: 10.1017/9781108877855

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Title: London Mathematical Society lecture note series
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Pages: - Volume / Issue: 473 Sequence Number: - Start / End Page: - Identifier: -