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@article{Connes2024,

title = {On the metaphysics of F1},

author = {Alain Connes and Caterina Consani },

editor = {Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 35 (2024), no. 1, 121-154},

url = {https://alainconnes.org/wp-content/uploads/On-the-Metaphysics-of-F_12024-published.pdf},

year = {2024},

date = {2024-07-01},

urldate = {2024-07-01},

journal = {Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.},

volume = {35},

number = {1},

issue = {35},

pages = {121-154},

abstract = { In the present paper, dedicated to Yuri Manin, we investigate the general notion of rings of mathbbSleft[mun,+right]mathbb{S}left[mu_{n,+}right]mathbbSleft[mun,+​right]-polynomials and relate this concept to the known notion of number systems. The Riemann-Roch theorem for the ring mathbbZmathbb{Z}mathbbZ of the integers that we obtained recently uses the understanding of mathbbZmathbb{Z}mathbbZ as a ring of polynomials mathbbS[X]mathbb{S}[X]mathbbS[X] in one variable over the absolute base mathbbSmathbb{S}mathbbS, where 1+1=X+X21+1=X+X^21+1=X+X2. The absolute base mathbbSmathbb{S}mathbbS (the categorical version of the sphere spectrum) thus turns out to be a strong candidate for the incarnation of the mysterious mathbbF1mathbb{F}_1mathbbF1​.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}