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math.AG2026
The Absolute Twistor Line and the Geometry of
Alain Connes, Caterina Consani
We construct the absolute algebraic geometry of the compactification by amalgamating the affine absolute curve $(\text{Spec}\, \mathbf Z)_{\mat…
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…