Nikolai Durov, new approach to Arakelov geometry, arXiv:0704.2030v1, in this approach a ‘’generalized ring’‘ (including $\mathbb{F}_1$) is an operad

Anton Deitmar

James Borger

Lieven Le Bruyn

Oliver Lorscheid

Christoph Soulé

Bertrand Toen Toen, Michel Vaquie, under Spec(Z),arXiv:math/0509684v4, describes interesting relations between algebra over $\mathbb{F}_1$ and stable homotopy theory

Shai Haran, non-additive geometry, this commeents on the Rieman hypothesis and Weil’ s approach (Weil proved a statement called concerning the Riemann hypothesis for curves over finite fields) to it

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Stephan Alexander Spahn?.
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