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math.AG2026
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 …
math.NT2026
On the Jacobian of
Alain Connes, Caterina Consani
We interpret the structure of the adele class space of the rationals--and specifically its Riemann sector--as the natural monoidal extension of the Picard group of the arithmetic c…
math.NT2026
The Riemann Hypothesis: Past, Present and a Letter Through Time
Alain Connes
This paper, commissioned as a survey of the Riemann Hypothesis, provides a comprehensive overview of 165 years of mathematical approaches to this fundamental problem, while introdu…