152 citations · 1.1k across the 34 of their papers we have counts for
4 papers · 1 filter
Quasi-inner functions and local factors
Alain Connes, Caterina Consani
We introduce the notion of {\it quasi-inner} function and show that the product of ratios of local {-}factors {} over a finit…
Weil positivity and Trace formula, the archimedean place
Alain Connes, Caterina Consani
We provide a potential conceptual reason for the positivity of the Weil functional using the Hilbert space framework of the semi-local trace formula of the paper "Trace formula in…
Spectral truncations in noncommutative geometry and operator systems
Alain Connes, Walter D. van Suijlekom
In this paper we extend the traditional framework of noncommutative geometry in order to deal with spectral truncations of geometric spaces (i.e. imposing an ultraviolet cutoff in…
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…