The integers are conjectured to form an algebra over this object, which could allow a proof of the Riemann hypothesis.
This object is the basis of a branch of projective geometry designed to give apartments and buildings equal standing. Durov constructed this object as a commutative algebraic monad, and Borger used descent to construct it from nite elds. Pointed sets are vector spaces over this object, and Weyl groups are simple algebraic groups over it. The integers are conjectured to form an algebra over this object, which could allow a proof of the Riemann hypothesis. Any nite set is both an a ne space and a projective space over this object. For ten points, identify this hypothetical algebraic object which has characteristic one. 
This object is the basis of a branch of projective geometry designed to give apartments and buildings equal standing.
field with one element [accept anything indicating a eld with  characteristic one before read, accept F1, accept Fun, accept anything like the eld where zero equals one ] 