Segal’s Gamma rings and universal arithmetic

@article{Connes2020SegalsGR,
  title={Segal’s Gamma rings and universal arithmetic},
  author={Alain Connes and Caterina Consani},
  journal={arXiv: Algebraic Geometry},
  year={2020}
}
Segal's Gamma-rings provide a natural framework for absolute algebraic geometry. We use Almkvist's global Witt construction to explore the relation with J. Borger F1-geometry and compute the Witt functor-ring of Almkvist for the simplest Gamma-ring S. We prove that it is isomorphic to the Galois invariant part of the BC-system, and exhibit the close relation between Lambda-rings and the Arithmetic site. Then, we concentrate on the Arakelov compactification of Z which acquires a structure sheaf… 
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