# Absolute algebra and Segal's Gamma sets

@article{Connes2015AbsoluteAA, title={Absolute algebra and Segal's Gamma sets}, author={Alain Connes and Caterina Consani}, journal={arXiv: Algebraic Geometry}, year={2015} }

We show that the basic categorical concept of an s-algebra as derived from the theory of Segal's -sets provides a unied description of several constructions attempting to model an algebraic geometry over the absolute point. It merges, in particular, the ap- proaches using monods, semirings and hyperrings as well as the development by means of monads and generalized rings in Arakelov geometry. The assembly map determines a functorial way to associate an s-algebra to a monad on pointed sets. The…

## 10 Citations

SpecZ and the Gromov norm

- Mathematics
- 2019

We define the homology of a simplicial set with coefficients in a Segal’s Γ-set (s-module). We show the relevance of this new homology with values in s-modules by proving that taking as coefficients…

BC-system, absolute cyclotomy and the quantized calculus

- Mathematics
- 2021

We give a short survey on several developments on the BC-system, the adele class space of the rationals, and on the understanding of the ”zeta sector” of the latter space as the Scaling Site. The new…

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

- Mathematics
- 2018

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…

On Noetherian schemes over (C,⊗,1) and the category of quasi-coherent sheaves

- Mathematics
- 2015

Let (C,⊗,1) be an abelian symmetric monoidal category satisfying certain conditions and let X be a scheme over (C,⊗,1) in the sense of Toen and Vaquie. In this paper we show that when X is…

Riemann-Roch for Spec Z

- Mathematics
- 2022

We prove a Riemann-Roch formula for Arakelov divisors on Spec Z equating the integer valued Euler characteristic with a simple modiﬁca-tion of the traditional expression ( i.e. the degree of the…

On Noetherian schemes over (\mathcal{C},\otimes,1)$ and the category of quasi-coherent sheaves

- Mathematics
- 2015

Let $(\mathcal C,\otimes,1)$ be an abelian symmetric monoidal category satisfying certain conditions and let $X$ be a scheme over $(\mathcal C,\otimes,1)$ in the sense of To\"en and Vaqui\'{e}. In…

$\overline{Spec\mathbb Z}$ and the Gromov norm

- Mathematics
- 2019

We define the homology of a simplicial set with coefficients in a Segal's $\Gamma$-set ($\mathbf S$-module). We show the relevance of this new homology with values in $\mathbf S$-modules by proving…

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