field with one element, in wikipedia
Jacques Tits
Alain Connes
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, 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