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On the Absolute Geometry of
Alain Connes, Caterina Consani
A guiding principle in P. Scholze's -adic geometry asserts that the points of over an algebraically closed perfectoid field of characteristic …
Riemann-Roch for
Alain Connes, Caterina Consani
We prove a Riemann-Roch theorem of an entirely novel nature for divisors on the Arakelov compactification of the algebraic spectrum of the integers. This result relies on the intro…
Segal's Gamma rings and universal arithmetic
Alain Connes, Caterina Consani
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 c…
On Absolute Algebraic Geometry, the affine case
Alain Connes, Caterina Consani
We develop algebraic geometry for general Segal's Gamma-rings and show that this new theory unifies two approaches we had considered earlier on (for a geometry under Spec Z). The s…
and the Gromov norm
Alain Connes, Caterina Consani
We define the homology of a simplicial set with coefficients in a Segal's -set (-module). We show the relevance of this new homology with values in -module…
Homological algebra in characteristic one
Alain Connes, Caterina Consani
This article develops several main results for a general theory of homological algebra in categories such as the category of sheaves of idempotent modules over a topos. In the anal…