Characteristic 1, entropy and the absolute point (Q2904907)

In this article the authors give some connections from absolute mathematics working with the field with one element to idempotent analysis and tropical algebraic geometry, which enables them to understand the notion of the absolute point \(\mathrm{Spec}\;\mathbb F_1\). The authors explain how to adapt the construction of the Witt ring in positive characteristic to the limit case of characteristic one. They simplify their earlier results on the construction of the geometric realization of an \(\mathbb F_1\)-scheme, and extend their earlier computations of the zeta function to cover the case with torsion. In the final part of the paper, the authors test the computations of the zeta functions on elliptic curves.NEWLINENEWLINEFor the entire collection see [Zbl 1243.14002].